Q: An object of mass $$m = 1\ \text{kg} is $$attached to a spring with force constant $$k = 40\ \text{N/m}$$ and released from rest when the spring is stretched $$4\ \text{m}. $$What is the magnitude and direction of the force exerted on the object at this point? $$F = -kx$$

$$160\ \text{N}$$, toward equilibrium

Q: A spring with $$k = 40\ \text{N/m} is $$stretched by $$2\ \text{m}. $$What force does it exert on the attached object? $$F = -kx$$

$$80\ \text{N}$$, toward equilibrium

Q: A child drives a bumper car head-on into a rail, which exerts a force of $$2700\ \text{N}$$ for $$0.400\ \text{s}. $$What impulse is imparted by this force? $$J = F_{avg} \Delta t$$

$$1080\ \text{N} \cdot \text{s}$$

Question 1

Two children push on opposite sides of a door, both perpendicular to the door. Child 1 pushes with a force of 175 N at a distance of 0.700 m from the hinges. Child 2 pushes at a distance of 0.400 m. What force must Child 2 exert to keep the door from rotating? (Assume friction is negligible.)

$$	au = rF$$

Accepted Answer

$$306\ 	ext{N}$$

Question 2

An object of mass $$m = 1\ 	ext{kg} is $$attached to a spring with force constant $$k = 40\ 	ext{N/m}$$ and released from rest when the spring is stretched $$4\ 	ext{m}. $$What is the magnitude and direction of the force exerted on the object at this point?

$$F = -kx$$

Accepted Answer

$$160\ 	ext{N}$$, toward equilibrium

Question 3

A spring with $$k = 40\ 	ext{N/m} is $$stretched by $$2\ 	ext{m}. $$What force does it exert on the attached object?

$$F = -kx$$

Accepted Answer

$$80\ 	ext{N}$$, toward equilibrium

Question 4

At what point does the force exerted by a spring vanish?

Accepted Answer

At the equilibrium (natural) length of the spring

Question 5

A uniform beam of length $$L = 2.00\ 	ext{m} is $$supported by a cable at one end and friction at the other. The cable makes an angle $$	heta = 30^\circ$$ with the horizontal. The coefficient of static friction at point A is $$\mu_s = 0.560. $$What is the minimum distance $$x$$ from point A at which an additional weight $$2w$$ can be hung without causing the rod to slip?

Accepted Answer

$$x = \frac{\mu_s L}{1 + 2\mu_s}$$

Question 6

A child drives a bumper car head-on into a rail, which exerts a force of $$2700\ 	ext{N}$$ for $$0.400\ 	ext{s}. $$What impulse is imparted by this force?

$$J = F_{avg} \Delta t$$

Accepted Answer

$$1080\ 	ext{N} \cdot 	ext{s}$$

Question 7

A bumper car (mass $$200\ 	ext{kg}) $$initially moves at $$3.30\ 	ext{m/s}. $$After a $$1080\ 	ext{N} \cdot 	ext{s}$$ impulse in the opposite direction, what is its final velocity?

$$v_f = v_i + \frac{J}{m}$$

Accepted Answer

$$-2.10\ 	ext{m/s}$$

Question 8

A $$2650\ 	ext{kg}$$ cannon fires a $$16.0\ 	ext{kg}$$ shell at $$480\ 	ext{m/s} at$$ $$20.0^\circ$$ above the horizontal. What is the recoil velocity of the cannon?

Use conservation of momentum: $$m_{cannon} v_{cannon} = -m_{shell} v_{shell} \cos 	heta$$

Accepted Answer

$$-2.89\ 	ext{m/s}$$

Question 9

A $$1000\ 	ext{kg}$$ car moving east at $$20\ 	ext{m/s}$$ collides with a $$1500\ 	ext{kg}$$ van moving north at $$30\ 	ext{m/s}. If $$the wreckage moves together after the collision, what type of collision is this?

Accepted Answer

Perfectly inelastic

Question 10

For the car-van collision above, what is the final speed of the wreckage?

$$V_f = \frac{\sqrt{(m_1$ v_1$)^2$$ + ($$m_2$$ $$v_2)^2$}}{m_1$ + m_2$}$$

Accepted Answer

$$22.4\ 	ext{m/s}$$

Question 11

In the car-van collision, what is the direction of motion of the wreckage?

$$	heta = 	an$$^{-1}$$\left(\frac{m_2$ v_2$}{m_1$ v_1$}ight)$$

Accepted Answer

$$56.3^\circ$$\ north of east

Question 12

A ballistic pendulum consists of a $$2\ 	ext{kg}$$ block and a $$50\ 	ext{g}$$ bullet fired at $$120\ 	ext{m/s}. $$What kind of collision occurs when the bullet embeds in the block?

Accepted Answer

Perfectly inelastic

Question 13

In the ballistic pendulum collision, which quantity is conserved during the impact?

Accepted Answer

Linear momentum

Question 14

After the bullet embeds in the block, what is the speed of the block right after the collision?

$$m_{total} v = m_{bullet} v_{bullet}$$

Accepted Answer

$$2.94\ 	ext{m/s}$$

Question 15

As the block swings up after the ballistic pendulum collision, which quantity is conserved?

Accepted Answer

Mechanical energy

Question 16

Suppose you press a $$5\ 	ext{kg}$$ mass into a spring with $$k = 200\ 	ext{N/m}$$, compressing it by $$20\ 	ext{cm}. $$What is the speed of the mass right after it loses contact with the spring?

$$\frac{1}{2} k x^2$ = \frac{1}{2} m v^2$

Accepted Answer

$$1.26\ 	ext{m/s}$$

Question 17

A $$5\ 	ext{kg}$$ mass slides across a concrete floor with $$\mu_k = 0.4$$ after being released from a compressed spring. How far does it slide before coming to rest?

$$\frac{1}{2} m v^2$ = \mu_k m g d$$

Accepted Answer

$$0.41\ 	ext{m}$$

Question 18

You throw a $$57\ 	ext{g}$$ tennis ball at a door $$81\ 	ext{cm}$$ wide, open by $$30^\circ. $$The hinge exerts a constant frictional torque of $$0.5\ 	ext{N} \cdot 	ext{m}. To $$just barely close the door, what is the minimum speed you must throw the ball?

Use conservation of angular momentum and work-energy principle.

Accepted Answer

$$8.8\ 	ext{m/s}$$

Physics Study Guide: Springs, Elasticity, Equilibrium, Impulse, Momentum, Energy, Collisions, Rotations

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