Physics I: Final Exam Study Guide

What is the relationship between the angle of the incline and acceleration?

(a) gcosθ (b) mgsinθ *(c) gsinθ* (d) tanθg

Describe a conservative force. HINT: There are 2.

gravity & elastic

A thin hoop with a radius of 10cm and a mass of 3kg is rotating about its center with an angular speed of 3.5rad/s. What is its kinetic energy?

(a) 0.96J (b) 1.05J (c) 0.092J (d) 0.53J *(e) 0.18J* K = 1/2Iw^2 and use I for thin hoop

An object is under the influence of a force as represented by the force vs. position graph in the figure. What is the work done as the object moves from 0m to 4m?

(a) 0J (b) 40J (c) 70J *(d) 20J* (e) 30J W (for triangle) = 1/2bh W = (.5)(4m)(10N) W = 20J

A string is wound tightly around a fixed pulley whose radius is 5cm. As the string is pulled, the pulley rotates without slipping. What is the angular speed of the pulley when the string has a linear speed of 5 m/s?

(a) 10 rad/s *(b) 100 rad/s* (c) 25 rad/s (d) 20 rad/s (e) 50 rad/s

A compact disk rotates at 210 rpm. What is its angular speed in rad/s?

(a) 11 rad/s (b)660 rad/s (c) 45.3 rad/s (d) 69.1 rad/s *(e) 22 rad/s* rad/s = 210 rev/min x 2pirad/rev x 1min/60s

A 50kg box is being pushed along a horizontal surface. The coefficient of kinetic friction between the box and the ground is 0.35. What horizontal force must be exerted on the box for it to accelerate at 1.2 m/s^2?

(a) 116N *(b) 232N* (c) 172N (d) 60N (e) 491N Fy = ma = 0 Fx = ma F - Ff = ma F - (uK)(N) = ma F - (.35)(500) = (50)(1.2) F = (50)(1.2) + (.35)(500) F = 232N

An object is under the influence of a force as represented by the force vs. position graph in the figure. What is the work done as the object moves from 0m to 10m?

(a) 125J (b) 25J *(c) 100J* (d) 50J (e) 80J W (for a square) = bh W = (10m)(10N) = 100J

The horizontal and vertical components of the initial velocity of a football are 24 m/s and 7 m/s respectively. What is the initial velocity of the football?

(a) 17 m/s *(b) 25 m/s* (c) 625 m/s (d) 42 m/s (e) 31 m/s R = sqrt of (24)^2 + (7)^2 R = 25 m/s

An object of mass 2 kg is held at the top of a triangular wedge as shown in the figure, and then released. The reference level for potential energy is at the base of the triangle. Neglect friction and use g = 10m/s^2. What is the speed of the object just before it reaches the bottom of the wedge?

(a) 2 m/s (b) 6 m/s (c) 0 m/s *(d) 8 m/s* (e) 10 m/s Ei = Ef, conservation of energy mgh = 1/2mv^2 (2)(10)(3) = (.5)(2)v^2 v = 8 m/s

The moment of inertia of a uniform rod (about its center) is given by I = ML 2/12. What is the kinetic energy of a 120cm rod with a mass of 450g rotating about its center at 3.6rad/s?

(a) 2.1J (b) 4.2J (c) 0.35J (d) 0.7J (e) 0.96J K = 1/2Iw^2 and use I for rod

How much energy is needed to change the speed of a 1600kg sport utility vehicle from 15 m/s to 40 m/s?

(a) 20 kJ (b) 10 kJ *(c) 1.1 MJ* (d) 0.96 MJ (e) 40 kJ KE = 1/2mv^2 initial KE = (.5)(1600)(15m/s) = 180,000J final KE = (.5)(1600)(40m/s) = 1,280,000J 1,280,000J - 180,000J = 1,100,000J -> 1.1MJ

A person applies a constant force of 20N to a rock of mass 1000kg, for a total of 20 seconds. What is the work done by this person if the rock does not move at all by this applied force?

(a) 20,000J *(b) 0J* (c) 400J (d) 1000J (e) 2000J

A constant force of 100N is applied to a mass of 40kg as shown in the figure. The force causes a displacement of 20m to this mass along the +x-axis. Neglect friction. What is the work done by the component of the force in the figure along the +x-axis?

(a) 2000J (b) 1680J (c) 2000J (d) 1520J *(e) 1530J* W = Fcos(theta)s W = (100N)cos(40degrees)(20m) W = 1532J

A 3kg and 5kg box rest side-by-side on a smooth, level floor. A horizontal force of 32N is applied to the 3kg box pushing it against the 5kg box and, as a result, both boxes slide along the floor. How large is the contact force between the two boxes?

(a) 24N *(b) 20N* (c) 12N (d) 32N (e) 0N

Block A has a mass of 3.4kg and rests on a smooth table and is connected to Block B, which has a mass of 1.6kg, after passing over an ideal pulley, as shown. Block Bis released from rest. What is the acceleration of the masses?

(a) 3.22 m/s^2 (b) 6.54 m/s^2 *(c) 3.14 m/s^2* (d) 5.1 m/s^2 (e) 8.24 m/s^2 use F = ma for x and y directions then add Fx for block A to Fy for block B to get a

A 1000kg car is moving at 30 m/s around a horizontal curve whose radius is 100m. What is the magnitude of the frictional force required to keep the car from sliding?

(a) 3000N (b) 9810N (c) 900N *(d) 9000N* (e) 300N

A wheel that is rotating at 33.3 rad/s is given an angular acceleration of 2.15 rad/s^2. Through what angle has the wheel turned when its angular speed reaches 72 rad/s?

(a) 316 rad *(b) 948 rad* (c) 697 rad (d) 83.2 rad (e) 66.8 rad (theta)f^2 = (theta)i^2 + 2as 5184 - 1109 = 2(2.15)s s = 948 rad

Block A has a mass of 5kg, Block B has a mass of 3kg and Block C has a mass of 2kg. The pulleys are ideal and there is no friction between Block B and the table. What is the tension in the string connecting blocks A and B?

(a) 38.3N (b) 25.5N *(c) 34.3N* (d) 20.6N (e) 13.7N

A spring with a spring constant of 2500 N/m is stretched 4 cm. What is the work required to stretch the spring?

(a) 3J (b) 0J (c) 4J (d) 1J *(e) 2J* U = 1/2Kx^2 U = (.5)(2500N/m)(.04m)^2 = 2J

Consider two uniform solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is...

(a) 4 (b) 2 (c) 1/2 (d) 10 (e) 6 *(f) 8*

A constant force of 20N is applied to an object of mass 8kg at an angle of 25 degrees with the horizontal. What is the work done by this force on the object if it causes a displacement of 2m along the horizontal direction?

(a) 40J (b) 0J *(c) 36J* (d) 17J (e) 19J W = Fcos(theta)s W = (20N)cos(25)(2m) W = 36.2J

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s^2. Through what angle does the pulley turn in 5.26s?

(a) 42.6 rad (b) 19.3 rad (c) 160 rad *(d) 113 rad* (e) 22.6 rad

A roller coaster of mass 80kg is moving with a speed of 20 m/s at position A as shown in the figure. The vertical height at position A above ground level is 200m. Neglect friction and use g = 10 m/s^2. What is the speed of the roller coaster at point C?

(a) 69.2 m/s (b) 0 m/s (c) 20 m/s *(d) 34.6 m/s* (e) There is not enough information to solve this problem

An object is under the influence of a force as represented by the force vs. position graph in the figure. What is the work done as the object moves from 4m to 6m?

(a) 70J *(b) 20J* (c) 40J (d) 30J (e) 0J W (for a square) = bh W = (2m)(10N) = 20J

An object of mass 2 kg is held at the top of a triangular wedge as shown in the figure, and then released. The reference level for potential energy is at the base of the triangle. Neglect friction and use g = 10m/s^2. What is the kinetic energy of the object at the top of the wedge?

(a) 80J (b) 30J (c) 60J (d) 40J *(e) 0J* there is no kinetic energy at the top of a path

An object of mass 4kg is thrown vertically upwards from ground level with an initial speed of 20 m/s. Ignore friction and use g = 10 m/s^2. How high did the object go?

(a) 80m (b) 4.5m (c) 15m *(d) 20m* (e) None of the other choices are correct Ei = Ef 1/2mv^2 = mgh (.5)(4)(20 m/s)^2 = (4)(10)h h = 20m

What does the slope of the line represent on the graph that plots acceleration vs. sinθ?

(a) 9.8 m/s *(b) acceleration caused by gravity* (c) 9.8 ft/s^2 (d) nothing

Which object has larger kinetic energy: a 500kg object moving with a speed of 40 m/s or 1000kg object moving at 20 m/s?

(a) Both have same kinetic energy *(b) The 500kg object moving at 40 m/s* (c) The 1000kg object moving at 20 m/s (d) Kinetic energy is independent of mass (e) Kinetic energy is independent of speed

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than Child B. Which child has the larger angular displacement?

(a) Child A (b) Child B (c) They have the same zero angular displacement *(d) They have the same non-zero angular displacement* (e) There is not enough information given

It is more difficult to start moving a heavy carton from rest than it is to keep pushing it with constant velocity, because...

(a) Initially, the normal force is not perpendicular to the applied force (b) The normal force is greater when the carton is at rest (c) Us < Uk (d) Us = Uk *(e) Us > Uk*

An elastic collision of two objects is characterized by the following...

(a) Total momentum of the system is conserved (b) Total kinetic energy of the system remains constant *(c) Both A and B are true* (d) Neither A nor B are true

A force F acting on an object of mass m causes a displacement d. The angle between these two vectors is θ. The work W done on that object is expressed by...

(a) W = Fdcotθ (b) W = Fd (c) W = Fdsinθ (d) W = Fdtanθ *(e) W = Fdcosθ*

You need to load a crate of mass m onto the bed of a truck. One possibility is to lift the crate straight up over a height h, equal to height of the truck's bed. The work done in this case is W1. The other possibility is to slide the crate up the frictionless ramp of length L as shown in the figure. In this case, you perform work W2. What statement is true?

(a) W1 > W2 (b) W1 < W2 *(c) W1 = W2* (d) No simple relationship exists between W1 and W2

Should the mass of the cart affect its acceleration?

(a) Yes, it increases its acceleration (b) Yes, it decreases its acceleration *(c) Its mass has no affect* (d) The acceleration is not constant

Which one of the following equations can be used to determine the acceleration of the cart down the incline?

(a) a = sqrt of 2d/t^2 (b) d = (at^2) (c) a = d/t (d) d = at *(e) none of the above*

What does the slope of the position vs. time graph for an inclined plane represent ?

(a) acceleration (b) friction *(c) instantaneous velocity* (d) final velocity

Two equal forces are applied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door/ Which force exerts the greater torque?

(a) both exert zero torques *(b) the second at the doorknob* (c) both exert equal non-zero torques (d) the first at the midpoint (e) additional information is needed

What is the shape of the velocity vs. time graph of an inclined plane?

(a) circular (b) parabolic *(c) straight line* (d) horizontal line

A constant net force acts on an object. Describe the motion of the object.

(a) constant non-zero velocity *(b) constant non-zero acceleration* (c) increasing acceleration (d) zero acceleration (e) decreasing acceleration

As the cart moves down the track, its acceleration...

(a) decreases (b) increases *(c) remains constant* (d) is 9.8 m/s^2

A pilot drops a bomb from a plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground, the horizontal location of the plane will...

(a) depend on the speed of the plan when the bomb was released (b) depend of the mass of the bomb when it was released (c) be in front of the bomb *(d) be over the bomb* (e) be behind the bomb

Which of the following graphs of the movement of the carts down the incline would produce a linear relationship?

(a) distance vs. time *(b) velocity vs. time* (c) time vs. distance (d) mass vs. distance

A uniform solid sphere has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central axis?

(a) increases by a factor of 54 *(b) increases by a factor of 18* (c) increases by a factor of 6 (d) increases by a factor of 5 (e) increases by a factor of 12

If the angle of the incline were increased, which of the following would also increase?

(a) initial velocity *(b) acceleration* (c) the time for the trip down the incline (d) none of the above

When the mass riding in the cart is increased, what should happen to the acceleration of the cart?

(a) it increases (b) it decreases *(c) it remains constant* (d) it reaches 9.8 m/s

When a car goes around a curve, it has a tendency to skid outwards. Is the frictional force between the tires and the ground that keeps the car from skidding kinetic or static?

(a) kinetic *(b) static*

What is the quantity used to measure an object's resistance to changes in rotational motion?

(a) mass (b) angular acceleration *(c) moment of inertia* (d) angular velocity (e) torque

An object is released from rest at a height h above the ground. A second object with four times the mass of the first is released from the same height. The potential energy of the second object compared to the first is...

(a) one-half as much (b) one-fourth as much *(c) four-times as much* (d) twice as much (e) eight times as much U = mgh since g & h are the same for both, they are cancelled and Ug for mass 2 ends up being 4x more

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three are released simultaneously at the top of an inclined plane, which will reach the bottom first?

(a) pipe (b) cylinder *(c) sphere* (d) they all reach the bottom at the same time (e) it depends on the angle of inclination

Which of the following changes in the experiment will affect the acceleration of the cart down the track?

(a) shorten the track (b) increase the mass of the cart *(c) increase the angle of the track* (d) use a smaller mass cart

We know that the acceleration of the carts down the incline is constant because...

(a) the slope of the distance graph is constant (b) the slope of the velocity graph keeps changing (c) the slope of the velocity graph is increasing *(d) the shape of the velocity graph is linear*

Which of the following graphs for an inclined plane would have a Curve Fit (trend line) that would be a quadratic?

(a) velocity vs. time *(b) distance vs. time* (c) time vs. velocity (d) acceleration vs. time

The angle of the ramp...

(a) was not important (b) was only important when large masses were involved in the trial (c) had no affect on the time it took the cart to get down the ramp *(d) affected the acceleration*

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s^2. Through what angle does the pulley turn in 5.26s?

*(a) 113 rad* (b) 22.6 rad (c) 160 rad (d) 19.3 rad (e) 42.6 rad solve for Wf first and then solve for angle

How long does it take a wheel that is rotating at 33.3 rpm to speed up to 78 rpm if it has an angular acceleration of 2.15 rad/s^2?

*(a) 2.18s* (b) 5.2s (c) 4.75s (d) 20.8s (e) 10.4s

How long does it take for a rotating object to speed up from 15 to 33.3 rad/s if it has an angular acceleration of 3.45 rad/s^2

*(a) 5.3s* (b) 9.57s (c) 4.35s (d) 63.1s (e) 10.6s α = △w/△t t = △w/α t = 33.3-15/3.45 t = 5.3s

An object of mass 10kg is initially at rest. A 100N force causes it to move horizontally through a distance of 6m. What is the change in the kinetic energy of this object?

*(a) 600J* (b) 0J (c) 200J (d) 60J (e) 1000J a = F/m = 100N/10kg = 10 m/s^2 then, Vf^2 = Vi^2 + 2a(Xf - Xi) Vf^2 = 0 + 2(10m/s^2)(6m-0m) Vf = 11 m/s finally, K = 1/2mv^2 K = (.5)(10kg)(10m/s^2) K = 600J

An object of mass 2 kg is held at the top of a triangular wedge as shown in the figure, and then released. The reference level for potential energy is at the base of the triangle. Neglect friction and use g = 10m/s^2. What is the gravitational potential energy of the object at the top of the wedge?

*(a) 60J* (b) 40J (c) 30J (d) 100J (e) 80J U = mgh U = (2kg)(10m/s^2)(3m) = 60J

A person drops a brick form the top of a building. The height of the building is 400m and the mass of the brick is 2kg. What will be the speed of the brick right before it touches the ground? Use g = 10 m/s^2

*(a) 89.4 m/s* (b) 10 m/s (c) 59.4 m/s (d) 63.2 m/s (e) 13.2 m/s Ei =Ef mgh = 1/2mv^2 (2)(10)(400) = (.5)(2)v^2 v = 89.4 m/s

What is the slope of the velocity vs. time graph of an inclined plane?

*(a) 9.8 m/s^2* (b) distance (c) final velocity *(d) acceleration*

An artillery shell explodes in midair and breaks up into many fragments. Which of the following statements are true regarding conditions immediately before and immediately after the explosion: I. The total momentum of the fragments is equal to the original momentum of the shell. II. The total kinetic energy of the fragments is equal to the original kinetic energy of the shell.

*(a) Statement I only* (b) Statement II only (c) Both I and II (d) Neither

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. Which object reaches the bottom of the incline first?

*(a) The disk* (b) The hoop (c) Both reach the bottom at the same time (d) It depends on the angle of inclination (e) It depends on the length of the inclined surface

What type of acceleration does an object moving with constant speed in a circular path experience?

*(a) centripetal acceleration* (b) terminal acceleration (c) free fall (d) linear acceleration (e) constant acceleration

A figure skater is spinning slowly with arms outstretched. She brings her arms in close to her body and her angular speed increases dramatically. The speed increase is a demonstration of...

*(a) conservation of angular momentum: her moment of inertia is decreased, and so her angular speed must increase to conserve angular momentum* (b) Newton's 2nd Law for rotational motion: she exerts a torque and so her angular speed must increase to conserve energy (c) conservation of energy: her moment of inertia is decreased, and so her angular speed must increase to conserve energy (d) this has nothing to do with mechanics, it is simply a result of her natural ability to perform

A person sits on a freely spinning lab stool (no friction). When this person extends her arms...

*(a) her moment of inertia increases and her angular velocity decreases* (b) her moment of inertia decreases and her angular velocity decreases (c) her moment of inertia decreases and her angular velocity increases (d) her moment of inertia increases and her angular velocity increases (e) her moment of inertia increases and her angular velocity remains the same

What is the correct expression for torque, in terms of the magnitude of the force, F, the radial distance from the axis of rotation, r, and the angle between the force and the radial line, theta?

*(a) t = Frsinθ* (b) t = Frθ (c) t = Frcotθ (d) t = Frcosθ (e) t = Frtanθ

On a force vs. position graph, the area under the curve is a representation of...

*(a) work* (b) position (c) kinetic energy (d) potential energy (e) force

Express an angle of 35.2 rad in degrees

*2,017 degrees* degrees = 35.2 rad x 180/pi

Express an angular speed of 33.3 rpm in rad/s

*3.5 rad/s* rad/s = 33.3 rev/min x 2pirad/rev x 1min/60s

Express an angle of 450 degrees in radians.

*7.85 rad* radians = 450 degrees x pi/180

Two masses are connected by a string which goes over an ideal pulley as shown in the figure. Block A has a mass of 3kg and can slide along a rough plane inclined 30 degrees to the horizontal. The coefficient of static friction between Block A and the plane is 0.4. What mass should Block B have in order to start Block A sliding up the ramp?

2.54kg

A hollow cylinder and a solid cylinder are constructed so they have the same mass and radius. Which cylineder has the larger moment of inertia?

hollow cylinder

A 55kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.3. What horizontal force must be applied to the box for it to start sliding along the surface?

F = uN F = (.3)(9.8m/s^2)(55kg) = *162N*

A flatbed truck is carrying a 20kg crate along a level road. The coefficient of static friction between the crate and the bed is 0.4. What is the max acceleration that the truck can have if the crate is to stay in place?

F = uN F = (.4)(20kg)(9.8m/s^2) = 78.4N F = ma 78.4N = (20kg)a a = *3.92 m/s^2*

Internal forces cannot change the total kinetic energy of a system. TRUE OR FALSE?

FALSE

The frictional force is a conservative force. TRUE OR FALSE?

FALSE

When a rigid body rotates about a fixed axis, all the points in the body have the same tangential speed. TRUE OR FALSE?

FALSE

A particle that has zero momentum must also have zero kinetic energy. TRUE OR FALSE?

TRUE

Any location can be chosen for potential energy to equal zero. TRUE OR FALSE?

TRUE

Internal forces cannot change the total momentum of a system. TRUE OR FALSE?

TRUE

Linear momentum is a vector quantity. TRUE OR FALSE?

TRUE

The banking angle for a properly banked curve does not depend on the mass of the car going over it. TRUE OR FALSE?

TRUE

The force for static friction between two surfaces is parallel to the surface of contact, and in the direction that opposes relative motion. TRUE OR FALSE?

TRUE

The gravitational force is a conservative force. TRUE OR FALSE?

TRUE

The horizontal component of the velocity of a projectile remains constant during the entire trajectory of the projectile. TRUE OR FALSE?

TRUE

The vertical component of the acceleration of a projectile remains constant during the entire trajectory of the projectile. TRUE OR FALSE?

TRUE

When a rigid body rotates about a fixed axis, all the points in the body have the same angular displacement. TRUE OR FALSE?

TRUE

What distinguishes a conservative force from a non-conservative force?

The path that work is done on.