Q: A sphere hangs suspended by a light string, resting against a vertical wall. The sphere has a mass of 2 kg and the string makes an 80° angle with the horizontal. What is the force from the wall against the ball?

$$F_{\text{wall}} = 3.5 \text{ N}$$

Q: Three horizontal forces act on a box (mass = 8 kg) sitting on a smooth surface: $$F_1 = 30$$ \text{ N}$$ at 53° counterclockwise from the +x axis, F_2$ = 13 \text{ N} at 67.4$$° clockwise from the +x axis, and $$F_3 = 20$$ \text{ N}$$ directly along the -x axis. What are the magnitude and direction of the box's acceleration?

$$a = 1.5 \text{ m/s}^2$$, 14° ccw from +x-axis

Q: The Mars Rover Perseverance weighed about 10,000 N while on Earth. After it reached the surface of Mars, it weighed about 3790 N. What is the gravitational acceleration on Mars?

$$g_{\text{Mars}} = 3.7 \text{ m/s}^2$$

Q: A 5.1 kg block is at rest on the floor. The coefficients of static & kinetic friction are $$\mu_s = 0.7$$ and $$\mu_k = 0.5. $$Calculate the force needed to get the block moving, and the force needed to keep it moving at constant speed.

$$F = 35.0 \text{ N}; F = 25.0 \text{ N}$$

Question 1

An object is said to be in equilibrium if which of the following conditions is true?

Accepted Answer

The net force acting on the object is zero ($$\sum F = 0)$$

Question 2

A 2 kg book rests on a table. What is the magnitude of the normal force acting on the book?

Accepted Answer

$$N = 19.6 	ext{ N}$$

Question 3

A 3-kg box is being lowered on a string at a constant speed. What is the tension in the string?

Accepted Answer

$$T = 29.4 	ext{ N}$$

Question 4

A loudspeaker is held in place by four vertical cables. The tension in each cable is 30 N. What is the mass of the loudspeaker?

Accepted Answer

$$m = 12.2 	ext{ kg}$$

Question 5

A 5 kg box is suspended in place by two cables. If both cables make a 30° angle with the vertical and the tension in each cable is 50 N, what is the mass of the chandelier?

Accepted Answer

$$m = 8.8 	ext{ kg}$$

Question 6

A traffic signal is suspended from three cables. The angles of the upper cables are $$\$$theta_1$$ = 22^	ext{\circ}$$ and $$\$$theta_2$$ = 60^	ext{\circ}. If $$the mass of the traffic signal is 8 kg, what is the tension in cable 1?

Accepted Answer

$$T_1 = 39.6$$ 	ext{ N}$$

Question 7

A sphere hangs suspended by a light string, resting against a vertical wall. The sphere has a mass of 2 kg and the string makes an 80° angle with the horizontal. What is the force from the wall against the ball?

Accepted Answer

$$F_{	ext{wall}} = 3.5 	ext{ N}$$

Question 8

Three horizontal forces act on a box (mass = 8 kg) sitting on a smooth surface: $$F_1 = 30$$ 	ext{ N}$$ at 53° counterclockwise from the +x axis, F_2$ = 13 	ext{ N} at 67.4$$° clockwise from the +x axis, and $$F_3 = 20$$ 	ext{ N}$$ directly along the -x axis. What are the magnitude and direction of the box's acceleration?

Accepted Answer

$$a = 1.5 	ext{ m/s}^2$$, 14° ccw from +x-axis

Question 9

A 5.1 kg block on the floor is pulled by a 10 N force 37° above the horizontal. Assuming no friction, what is the normal force on the block?

Accepted Answer

$$N = 39.6 	ext{ N}$$

Question 10

You push a 5.1 kg cart along the floor with an unknown force $$F at 30$$° below the horizontal. Using a scale, you know the normal force is 70 N. What is the horizontal acceleration of the cart?

Accepted Answer

$$a = 3.92 	ext{ m/s}^2$$

Question 11

You drop a 2-kg box straight down from the top of a building. A steady horizontal wind exerts a constant force of 3 N on the box as it falls. What is the direction of the box's acceleration?

Accepted Answer

8.7° below horizontal

Question 12

The Mars Rover Perseverance weighed about 10,000 N while on Earth. After it reached the surface of Mars, it weighed about 3790 N. What is the gravitational acceleration on Mars?

Accepted Answer

$$g_{	ext{Mars}} = 3.7 	ext{ m/s}^2$$

Question 13

A 3-kg bucket is being pulled upwards by a cord. The tension in the cord is 35 N. What is the acceleration of the bucket?

Accepted Answer

$$a = 1.9 	ext{ m/s}^2$$

Question 14

A 100-kg load of bricks is being lowered down on a cable at a speed of 5 m/s. If the load takes 2 s to slow from that speed to a stop, what is the tension in the supporting cable during that time interval?

Accepted Answer

$$T = 1230 	ext{ N}$$

Question 15

Pushing a 10-kg toolbox across the floor, you find that the box moves at a constant speed when you push horizontally with a force of 39 N. What is the coefficient of kinetic friction between the floor and the toolbox?

Accepted Answer

$$\mu_k = 0.4$$

Question 16

You push on a 3-kg box to give it an initial speed of 5 m/s across a floor. If $$\mu_k = 0.3$$, how far does the box travel before coming to a stop?

Accepted Answer

$$d = 7.7 	ext{ m}$$

Question 17

A 20-kg box moving along the floor has a downward force of 30 N acting on it. How hard must you push the box horizontally to keep the box moving at a constant 2 m/s if the coefficient of kinetic friction $$\mu_k is 0.3$$?

Accepted Answer

$$F = 67.8 	ext{ N}$$

Question 18

A 5.1 kg block is at rest on the floor. The coefficients of static & kinetic friction are $$\mu_s = 0.7$$ and $$\mu_k = 0.5. $$Calculate the force needed to get the block moving, and the force needed to keep it moving at constant speed.

Accepted Answer

$$F = 35.0 	ext{ N}; F = 25.0 	ext{ N}$$

Question 19

An 800-kg car is traveling along a horizontal road directly towards a cliff. The driver brakes, resulting in a 5,000-N net force slowing the car down. If the car's initial speed was 20 m/s and the car stops just before going over the cliff, how far away was the car from the cliff when the driver hit the brakes?

Accepted Answer

$$d = 64 	ext{ m}$$

Question 20

A 1000-kg rocket is taking off from rest, accelerating vertically upward. During the first 20 seconds, the force of gravity is 10,000 N (down), the engines provide 25,000 N of thrust (up), and air resistance is 5,000 N (down). What is the rocket's velocity after 20 s?

Accepted Answer

$$v = 200 	ext{ m/s}$$

Dynamics I: Motion Along a Line – Comprehensive Study Notes

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