Lab Tests

Which one of the following statements is correct for an object in mechanical equilibrium? (A) An object is in mechanical equilibrium if and only if the net external force on the object is zero and the net external torque on the object is zero. (B) An object is in mechanical equilibrium as long as the net external torque on the object is zero. The net external force can have any value. (C) An object is in mechanical equilibrium as long as the net external force on the object is zero. The net external torque can have any value.

(A) An object is in mechanical equilibrium if and only if the net external force on the object is zero and the net external torque on the object is zero.

Consider an object (your phone, for example) that is at rest and remains at rest. Which one of the following statements is correct? (A) Both the net force and the net torque on the object must be zero. (B) The net torque on the object must be zero, but the net force on it may or may not be zero. (C) The net force on the object must be zero, but the net torque on it may or may not be zero.

(A) Both the net force and the net torque on the object must be zero.

Consider a force of magnitude F acting at a lever arm distance of d from an axis of rotation. The resulting torque is 4 N·m. If the magnitude of the force is changed to 2F and its lever arm distance is changed to 2d, then which one of the following values is the new torque? (A) 16 N·m (B) 1 N·m (C) 2 N·m (D) 8 N·m (E) 4 N·m

(A) 16 N·m

Consider a uniform beam balancing on a pivot point at its centre (i.e. a see-saw). If a vertically-downward force of 10 N is acting on the beam at a distance of 2 m to the left of the pivot, where must a vertically-upward force of 20 N act in order for the beam to remain in mechanical equilibrium? (A) The vertically-upward force of 20 N must act at a distance of 1 m, also to the left of the pivot. (B) The vertically-upward force of 20 N must act at a distance of 4 m to the right of the pivot (C) The vertically-upward force of 20 N must act at a distance of 1 m to the right of the pivot. (D) The vertically-upward force of 20 N must act at a distance of 4 m, also to the left of the pivot.

(A) The vertically-upward force of 20 N must act at a distance of 1 m, also to the left of the pivot.

In lab M39 you attempted to verify the conditions for mechanical equilibrium by analysing the forces and torques acting on a rigid bar. You chose the axis of rotation to be the centre of the bar, so that the torque due to the weight of the bar was zero. Would it have been valid to choose a different location for the axis of rotation? i.e. Would the experiment still have been valid if you had chosen the point of application of F1 (for example) to be the axis of rotation? (A) Yes. (B) No.

(A) Yes.

Suppose that in an experiment such as you have just completed, the speed of the ball just before it hit the pendulum cage, vi, was very accurately measured, the speed of the ball and pendulum cage, Vf, just after the collision was very accurately measured, and the masses of the ball, m, and pendulum bob, M, were accurately known. Which of the following could be reasons why the experiment might show that the initial momentum, mvi, was slightly different from the final momentum, (m + M)Vf? Select all that apply. (A) The mass of the rod holding the pendulum cage, while small, is not really zero. (B) There was some friction in the hinge on which the pendulum swung. (C) The air resistance was ignored during the ball's flight toward the pendulum cage. (D) Some energy is lost to heat and sound during the collision.

(A) The mass of the rod holding the pendulum cage, while small, is not really zero. (B) There was some friction in the hinge on which the pendulum swung.

Which of the following are things that it was necessary to ignore in our test of Newton's 1st Law with this experiment? Select all that apply. (A) The mass of the strings and the knot. (B) Friction in the pulleys. (C) Air resistance. (D) The fact that the acceleration due to gravity at the location of the experiment may have been different from the quoted value.

(A) The mass of the strings and the knot. (B) Friction in the pulleys.

Two forces are acting on an object. The forces are equal in magnitude and opposite in direction. Which one of the following statements is correct concerning the net torque on the object? (A) The net torque on the object may or may not be zero, depending on other parameters. (B) The net torque on the object cannot be zero. (C) The net torque on the object is zero.

(A) The net torque on the object may or may not be zero, depending on other parameters.

In your experiment you took great care to eliminate the effects of the external magnetic field existing in the room (mostly due the the Earth's magnetic field). This magnetic field was considered to be completely cancelled when the current in the Helmholtz coil was the value referred to as the zero reference current I0. Which of the following statements are correct when the current I0 flows through the Helmholtz coil? Select all that apply. (A) The orientation of the apparatus is such that the external magnetic field passes through the apparatus at right angles to the plane formed by one of the circular Helmholtz coils. (B) The orientation of the apparatus is such that the external magnetic field passes through the apparatus parallel to the plane formed by one of the circular Helmholtz coils. (C) The magnetic field generated by the Helmholtz coil has exactly two times the magnitude as the external magnetic field. (D) The magnetic field generated by the Helmholtz coil has the exact opposite direction as the external magnetic field. (E) The magnetic field generated by the Helmholtz coil has the same magnitude as the external magnetic field. (F) The magnetic field generated by the Helmholtz coil has the same direction as the external magnetic field.

(A) The orientation of the apparatus is such that the external magnetic field passes through the apparatus at right angles to the plane formed by one of the circular Helmholtz coils. (D) The magnetic field generated by the Helmholtz coil has the exact opposite direction as the external magnetic field. (E) The magnetic field generated by the Helmholtz coil has the same magnitude as the external magnetic field.

Consider the circuit shown in figure 5 that you used in your lab. Suppose you take another voltmeter and measure the voltage across the power supply (between the + and -) and you find a value VP. The voltage measured by the voltmeter across the resistance R3 is VR. Which of the following is a correct statement? (E7-Circuit2) (A) You could find that VP is greater than VR which would indicate that the resistance of the ammeter is not negligible. (B) You could find that VP is less than VR which would indicate that the resistance of the ammeter is not negligible. (C) You would always find that VP is equal to VR regardless of the resistance of the ammeter.

(A) You could find that VP is greater than VR which would indicate that the resistance of the ammeter is not negligible.

Suppose you connected the resistor box in the way shown in the diagram below. Assume that the wires have negligible resistance. You use the multimeter to measure resistance. What will you measure? (E7-circuit) (A) You will measure the resistance of R3. (B) You will measure zero resistance. (C) You will measure the resistance of R1 in series with R2 and R3. (D) You will measure the resistance of R1 in parallel with R2. (E) You will measure the resistance of R1 in parallel with R3. (F) You will measure the resistance of R1 in series with R2.

(A) You will measure the resistance of R3.

Referring to Figure 1 in the M3 laboratory manual, the x-component of the vector F ⃗_B is (A) -F_B tan⁡(θ_B) (B) -F_B cos⁡(θ_B) (C) -F_B sin⁡(θ_B) (D) +F_B tan⁡(θ_B) (E) +F_B cos⁡(θ_B) (F) +F_B sin⁡(θ_B)

(B) -F_B cos⁡(θ_B)

Three resistors, with values of 2.0, 4.0 and 8.0 ohms, respectively, are connected in parallel. What is the overall resistance of this combination? (A) 2.0 ohms (B) 1.1 ohms (C) 14.0 ohms (D) 0.9 ohms (E) 7.0 ohms

(B) 1.1 ohms

Suppose two resistors are connected in series. One resistor has a value of 472 ± 24 ohms and the other resistor has a value of 125 ± 13 ohms. Calculate the total resistance and tolerance for this series combination. (A) 99 ± 15 ohms (B) 597 ± 37 ohms (C) 99 ± 37 ohms (D) 597 ± 92 ohms (E) 347 ± 37 ohms

(B) 597 ± 37 ohms

If a certain resistor obeys Ohm's law, its resistance will change: (A) as both the voltage across the resistor and the current through the resistor change. (B) All other choices are wrong since resistance is a constant for the given resistor. (C) as the voltage across the resistor changes. (D) as the current through the resistor changes. (E) as the energy given off by the electrons in their collisions changes.

(B) All other choices are wrong since resistance is a constant for the given resistor.

Suppose that in your experiment with the ballistic pendulum the pendulum cage rose to a height H. Now suppose you repeated the experiment but this time you used a ball with twice the mass and the mass of the pendulum cage was increased to twice its original mass. However the spring launching the ball was adjusted so that the initial speed of the ball was the same as it was in your experiment. The height to which the pendulum cage rises in the repeated experiment would be... (A) 2H (B) H (C) ½ H (D) ¼ H (E) 4H (F) 1/16 H (G) 16H

(B) H

Consider two vectors, A and B, that are not co-linear. i.e. A and B are not in the same direction. If R is the vector that results from adding vectors A and B, which one of the following statements is correct concerning the magnitude of R in terms of the magnitudes of A and B? (A) R > A + B (B) R < A + B (C) R = A + B

(B) R < A + B

Refer to Figure 1 in the M3 lab manual. Suppose the mass mB (on the left) is larger than the mass mA (on the right). When the system is in equilibrium, which one of the following statements is correct? [Hint: Consider the horizontal components of the tension forces.] (A) The knot will be to the right of half way between the two pulleys and the angles θA < θB. (B) The knot will be to the left of half way between the two pulleys and the angles θA < θB. (C) The knot will be to the right of half way between the two pulleys and the angles θA > θB. (D) The knot will be half way between the two pulleys and the angles θA = θB. (E) The knot will be to the left of half way between the two pulleys and the angles θA > θB.

(B) The knot will be to the left of half way between the two pulleys and the angles θA < θB. Solution explanation: The horizontal component must be equal. So if FA < FB then θA < θB.

A proton and a deuteron are moving with equal velocities perpendicular to a uniform magnetic field. A deuteron has the same charge as the proton but has twice its mass. The ratio of the acceleration of the proton to that of the deuteron is: (A) 1 (B) There is no acceleration for proton and deuteron (C) 2 (D) 4 (E) 1/2

(C) 2

Consider an object on which two (and only two) forces are acting. Force 1 has a magnitude of 1.4 N and is directed vertically downward and Force 2 has a magnitude of 1.4 N and is directed horizontally to the right. The net force acting on the object is? (A) 2.0 N at an angle of 45° above the horizontal (up and to the left). (B) zero. (C) 2.0 N at an angle of 45° below the horizontal (down and to the right). (D) 1.4 N at an angle of 45° below the horizontal (down and to the right).

(C) 2.0 N at an angle of 45° below the horizontal (down and to the right).

Which one of the following expressions is not equivalent to the SI unit of magnetic field? (A) N/(C·m/s) (B) kg/(C·s) (C) J/(A·m)

(C) J/(A·m)

An object is said to be in static translational equilibrium if it is at rest and remains at rest. Consider an object on which two (and only two) forces are acting. Which one of the following conditions will ensure that the object remains in static translational equilibrium? (A) One of the forces has a much greater magnitude than the other. (B) The two forces are equal in magnitude and act in the same direction. (C) The two forces are equal in magnitude and act in opposite directions. (D) The two forces are equal in magnitude and act in perpendicular directions.

(C) The two forces are equal in magnitude and act in opposite directions.

An electron moves across the Earth's equator in a north-easterly direction. At this point the Earth's magnetic field has a direction due north and is parallel to the Earth's surface. What is the direction of the force acting on the electron at this instant? (A) toward the northwest (B) toward the southwest (C) into the Earth's surface (D) toward the northeast (E) out of the Earth's surface

(C) into the Earth's surface

A 1.00-kg duck is flying horizontally overhead at 1.50 m/s when a hunter fires straight up. The 10-g bullet is moving vertically at a speed of 100 m/s when it hits the duck and stays lodged in the duck's body. What is the speed of the duck and bullet immediately after the hit? (A) 2.48 m/s (B) 1.49 m/s (C) 1.80 m/s (D) 1.36 m/s (E) 1.78 m/s

(E) 1.78 m/s

A neutron in a nuclear reactor makes an elastic head-on collision with a carbon atom initially at rest. (The mass of the carbon atom is 12 times that of the neutron.) What fraction of the neutron's kinetic energy is transferred to the carbon atom? (i.e. Calculate the ratio of the final kinetic energy of the carbon atom to the initial kinetic energy of the neutron. HINT: Use the same approach as you used for the derivation in the tutorial.) (A) 41.4% (B) 14.2% (C) 56.8% (D) 34.6% (E) 28.4%

(E) 28.4%

The inside edge of the visible electron beam appears fuzzy. Which one of the following statements is the best explanation of this? (A) Electrons that have undergone a collision have lost some of their speed and therefore the radius of their trajectory is larger. (B) Electrons that have undergone a collision have lost some of their mass and therefore the radius of their trajectory is larger. (C) Electrons that have undergone a collision have lost some of their mass and therefore the radius of their trajectory is smaller. (D) Electrons that have undergone a collision have gained some energy and therefore the radius of their trajectory is smaller. (E) Electrons that have undergone a collision have lost some of their speed and therefore the radius of their trajectory is smaller. (F) Electrons that have undergone a collision have gained some energy and therefore the radius of their trajectory is larger.

(E) Electrons that have undergone a collision have lost some of their speed and therefore the radius of their trajectory is smaller.

In an inelastic collision between two objects with unequal mass: (A) the total momentum of the system will decrease. (B) the energy of one increases by the amount that the energy of the other decreases. (C) the velocity of one will increase by the amount that the velocity of the other decreases. (D) the kinetic energy of one will increase by the amount that the kinetic energy of the other decreases. (E) the momentum of one will increase by the amount that the momentum of the other decreases.

(E) the momentum of one will increase by the amount that the momentum of the other decreases.

You measure the voltage versus current for a resistor network and obtain the graph shown below. However, instead of the resistor network being just a single resistance (as you did in step one of your lab) it consists of two identical resistors wired in parallel. What is the resistance of one of the resistors? (E7-Ohm diagram) (0.010A, 3.0V); (0.020A, 6.0V)

600 ohms