PHYSICS-EXAM2
8.7.3. The Jensens decided to spend their family vacation white water rafting. During one segment of their trip down a horizontal section of the river, the raft (total mass = 544 kg) has an initial speed of 6.75 m/s. The raft then drops a vertical distance of 14.0 m, ending with a final speed of 15.2 m/s. How much work was done on the raft by non-conservative forces?
-24200J Wnc=(kf+Uf)-(ki+vi) =(1/2m(15.2)^2-1/2m(6.75)^2-mg14 =544(115.52-22.78-77712.96 =50450.56-74712.96 =-24262.4 -Wnc=-24200J
7.7.2. In designing a spring loaded cannon, determine the spring constant required to launch a 2.0 kg ball with an initial speed of 1.2 m/s from a position where the spring is displaced 0.15 m from its equilibrium position.
128N/M Applying the Law of Conservation of Energy: Kinetic Energy=Energy stored in the spring 1/2mv^2=1/2kx^2 =k=mv^2/x^2 =k=2(1.2)^2/(0.15)^2 =k=128N/M
8.5.6. A quarter is dropped from rest from the fifth floor of a very tall building. The speed of the quarter is v just before striking the ground. From what floor would the quarter have to be dropped from rest for the speed just before striking the ground to be approximately 2v? Ignore all air resistance effects to determine your answer.
20 mg(5H)=1/2mv^2 mg(nH)=1/2m(2v)^2 (2)/(1): n/5=4 so n=20
8.5.3 Determine the amount of work done in firing a 2.0-kg projectile with an initial speed of 50m/s. Neglect any effects due to air resistance.
2500J 1/2mv^2 m=2.0kg v=50m/s 1/2(2.0)(50)=2500J
8.8.2 If the amount of energy needed to operate a 100W light bulb for one minute were used to launch a 2-kg projectile, what maximum height could the projectile reach, ignoring any resistive effects?
300m E=conserved (P)(1min)=mgH (100J/s)(60s)=(2)(9.8)H H=(100J/s)(60s)/[(2)(9.8)] H=306.12m
7.9.1. An SUV is accelerated from rest to a speed vin a time interval t. Neglecting air resistance effects and assuming the engine is operating at its maximum power rating when accelerating, determine the time interval for the SUV to accelerate from rest to a speed 2v.
4t P=E/t V1*1/2mv^2=E1t 2V1 1/2m(2v)^2=4*1/2mv^2=4E
8.5.5. You are investigating the safety of a playground slide. You are interested in finding out what the maximum speed will be of children sliding on it when the conditions make it very slippery (assume frictionless). The height of the slide is 2.5 m. What is that maximum speed of a child if she starts from rest at the top?
7.0m/s mgh=1/2mv^2 v=√ 2gh = √ 2*9.8*2.5 =7.0m/s
8.7.1 A car is being driven along a country road on a dark and rainy night at a speed of 20 m/s. The section of road is horizontal and straight. The driver sees that a tree has fallen and covered the road ahead. Panicking, the driver locks the brakes at a distance of 20 m from the tree. If the coefficient of friction between the wheels and road is 0.8, determine the outcome.
9.30m/s=As the car crashes into the tree, its speed is 9.3m/s Given: init veto of car= u =20m/s coefficient of friction between wheels & road is=μ=0.8 Distance= x=20m From Newtons 2nd law: ma=-μg =-(0.8)(9.80) =-7.84m/s^2 From the kinematics's equation: v=√ v^2+2ax =√ (20)^2+2(-7.84)(20) =9.295m/s, answer is 9.3m/s
Hw#5 In the figure, a crate of mass m = 84 kg is pushed at a constant speed up a frictionless ramp (θ = 29°) by a horizontal force ModifyingAbove Upper F With right-arrow. The positive direction of an x axis is up the ramp, and the positive direction of a y axis is perpendicular to the ramp. (a) What is the magnitude of F? (b) What is the magnitude of the normal force on the crate?
A: F=456.3N B: =941.2N A: since Fnet=Fapplied-Fweight=0 Fapplied=Fweight FCOS(29)=mgSIN(29) =F=mgTAN(29) =(84)(9.8)TAN(29)=F=456.3 B: N=mgCOS(29)+FSIN(29) =(84)(9.8)(COS(29))+456.3(SIN(29))=941.2N
In the figure, a 0.25 kg block of cheese lies on the floor of a 880 kg elevator cab that is being pulled upward by a cable through distance d1 = 2.9 m and then through distanced2 = 10.5 m. (a) Through d1, if the normal force on the block from the floor has constant magnitude FN = 3.14 N, how much work is done on the cab by the force from the cable? (b) Through d2, if the work done on the cab by the (constant) force from the cable is 93.46 kJ, what is the magnitude of FN?
A=32062.226J B=2.5279N A: given that Fn=3.14 to find a: 3.14/0.25 so a=12.56m/s^2 W=m*a*d1 (880+0.25)*12.56*2.9 W=32062.226J B: W=m*a*d2 (93.46*1000)=880.25*a*10.5 a=93.46*1000/880.25*10.5 a=10.1118m/s^2 Fn=0.25*a Fn=2.5279N
7.7.1. Block A has a mass m and block B has a mass 2m. Block A is pressed against a spring to compress the spring by a distance x. It is then released such that the block eventually separates from the spring and it slides across a surface where the friction coefficient is μk. The same process is applied to block B. Which one of the following statements concerning the distance that each block slides before stopping is correct?
Block A slides twice the distance that Block B slides. SPE=1/2kx^2 KE1=KE2 KE1=μkmg*XA KE2=μk*2mg*XB so, XA=2XB
6.3.1 Jennifer is pushing a heavy box up a rough inclined surface at a constant speed by applying a horizontal force F as show in the drawing. The coefficient of kinetic friction for the box on the inclined surface is uk. Which one of the following expressions correctly determines the normal force on the box?
Fn=Fcos()-mgsin()/uk **The normal force depends on both the weight and the applied force
7.6.3 Two balls of equal size are dropped from the same height from the roof of a building. One ball has twice the mass of the other. When the balls reach the ground, how do the kinetic energies of the two balls compare?
The lighter one has one half as much kinetic energy as the other does. KE1=2KE2
7.5.5 Two wooden blocks are sliding with the same kinetic energy across a horizontal frictionless surface. Block A has a mass m and block B has a mass 2m. At time t = 0 s, the blocks both slide onto a horizontal surface where the kinetic coefficient of friction between the blocks and surface is µk. Let xA represent the distance that block A slides before coming to a stop; and xB the distance that block B slides before it stops. Which one of the following expressions concerning these distances is correct?
XA=2XB K E of block A= K E of block B
6.5.9. At a circus, a clown on a motorcycle with a mass M travels along a horizontal track and enters a vertical circle of radius r. Which one of the following expressions determines the minimum speed that the motorcycle must have at the top of the track to remain in contact with the track?
v=√ gr
