Q: A child sled system is moving to the right and speeding up. The net force acting on the system is $$\vec{F}_{\text{net}} = F_{\text{net}}\,\hat{i} + 0\,\hat{j}. $$Which of the following best describes the direction of the net force?

$$\vec{F}_{\text{net}} = F_{\text{net}}\,\hat{i}$$

Q: A variable force $$F_{\text{exerted}}$$ acts on a mass $$m$$ and changes its velocity from $$v_0 to$$ $$v_f$$ over time $$\Delta t. $$What is the average force exerted during this interval?

$$F_{\text{average}} = \frac{m(v_f - v_0$)}{\Delta t}$$

Q: A $$5\,\mathrm{kg}$$ object is moving in a circle of radius $$2\,\mathrm{m} at a $$constant speed of $$4\,\mathrm{m/s}. $$What is the magnitude of the centripetal force acting on the object?

$$F_c = \frac{mv^2$}{r} = \frac{5 \times 16}{2} = 40\,\mathrm{N}$$

Question 1

A projectile is fired at an angle $$	heta$$ above the horizontal with initial speed $$v_0. $$Neglecting air resistance, which of the following statements is NOT true about its motion?

Accepted Answer

The component of velocity in the vertical direction is constant.

Question 2

A $$3.0\,\mathrm{kg}$$ projectile is fired into the air from the ground and lands at the same height from which it was launched. If its initial velocity is $$\vec{v}_0 = 7.8\,\hat{i} + 8.2\,\hat{j}\,\mathrm{m/s}$$, what is the speed of the projectile just before it hits the ground?

Accepted Answer

$$\sqrt{(7.8)^2$ + (8.2)^2$}\,\mathrm{m/s}$$

Question 3

Given the same projectile as above ($$\vec{v}_0 = 7.8\,\hat{i} + 8.2\,\hat{j}\,\mathrm{m/s}$$), what is the horizontal range of the projectile? (Assume $$g = 9.8\,\mathrm{m/s^2$})$$

Accepted Answer

$$12.8\,\mathrm{m}$$

Question 4

A projectile is at the apex of its trajectory when a wind gust with speed $$v_w = 12.3\,\mathrm{m/s}$$ hits it horizontally. What is the most likely effect on the projectile's motion?

Accepted Answer

Increase the horizontal component of velocity, increasing the range.

Question 5

A child sled system is moving to the right and speeding up. The net force acting on the system is $$\vec{F}_{	ext{net}} = F_{	ext{net}}\,\hat{i} + 0\,\hat{j}. $$Which of the following best describes the direction of the net force?

Accepted Answer

$$\vec{F}_{	ext{net}} = F_{	ext{net}}\,\hat{i}$$

Question 6

Two cases are considered: Case 1, a child pushes a sled horizontally; Case 2, a child pushes down on the sled at an angle. Which case will experience more friction force and why?

Accepted Answer

Case 2, because pushing down increases the normal force, increasing friction.

Question 7

A variable force $$F_{	ext{exerted}}$$ acts on a mass $$m$$ and changes its velocity from $$v_0 to$$ $$v_f$$ over time $$\Delta t. $$What is the average force exerted during this interval?

Accepted Answer

$$F_{	ext{average}} = \frac{m(v_f - v_0$)}{\Delta t}$$

Question 8

A $$20\,\mathrm{N}$$ bucket is at the bottom of a $$9\,\mathrm{m}$$ deep well and is initially at rest. The bucket is pulled to the top by a string that exerts a constant tension force such that it reaches the top in $$9.0\,\mathrm{s}. $$What is the tension in the string?

Accepted Answer

$$24\,\mathrm{N}$$

Question 9

A block of mass $$m$$ rests on a table. You apply a small force to the block, but it does not move. Which of the following is NOT a force acting on the block?

Accepted Answer

The block's push on the table and the table's push on the block

Question 10

A car is moving in a circle on a flat road. Which force provides the centripetal acceleration that keeps the car in circular motion?

Accepted Answer

Friction

Question 11

What is the maximum velocity that a car of mass $$m$$ can have in a curve of radius $$r$$ before it starts to skid, given the coefficient of static friction $$\mu_s$$?

Accepted Answer

$$v = \sqrt{\mu_s g r}$$

Question 12

If a car is taking a curve and the coefficient of static friction between the tire and road drops to zero, what will happen to the motion of the car?

Accepted Answer

The car will slide off the road increasing radius of the path due to tendency of object to maintain direction and magnitude of velocity.

Question 13

At the instant shown, three asteroids are in line, and the distance between A and B is the same as between B and C. Asteroids B and C have the same mass $$M$$, while asteroid A has twice the mass. A student states: “Asteroid A will attract Asteroid B with more force than Asteroid B will exert on Asteroid A because Asteroid A has bigger mass than Asteroid B.” Do you agree or disagree with the student?

Accepted Answer

Disagree because the force of attraction is directly proportional to the product of the masses and Newton's third law applies.

Question 14

What is the correct relationship between gravitational field strengths Asteroid A exerts on space at the positions of Asteroids B and C, $$g_B$$ and $$g_C$$ respectively?

Accepted Answer

$$g_B = 4g_C$$

Question 15

A $$5\,\mathrm{kg}$$ object is moving in a circle of radius $$2\,\mathrm{m} at a $$constant speed of $$4\,\mathrm{m/s}. $$What is the magnitude of the centripetal force acting on the object?

Accepted Answer

$$F_c = \frac{mv^2$}{r} = \frac{5 	imes 16}{2} = 40\,\mathrm{N}$$

Question 16

A $$2\,\mathrm{kg}$$ block is pulled across a horizontal surface with a force of $$10\,\mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal. If the coefficient of kinetic friction is $$\mu_k = 0.2$$, what is the acceleration of the block?

Accepted Answer

$$a = \frac{F \cos 	heta - \mu_k mg}{m}$$

Question 17

A $$1\,\mathrm{kg}$$ ball is dropped from a height of $$20\,\mathrm{m}. $$What is its speed just before it hits the ground? (Neglect air resistance)

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 20} \approx 19.8\,\mathrm{m/s}$$

Question 18

A $$0.5\,\mathrm{kg}$$ puck slides on ice with an initial velocity of $$6\,\mathrm{m/s}$$ and comes to rest after $$10\,\mathrm{m}. $$What is the magnitude of the friction force acting on the puck?

Accepted Answer

$$F = ma = m \frac{v^2$}{2d}$$

Projectile Motion, Forces, and Gravitation: Physics Study Notes

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