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Newton’s Second Law (more)

Solve the following problems using what you know about
Newton’s Laws and the four powerful equations. **Be careful**, some of the problems have multiple parts!

2.) d = v

3.) v

4.) v = v

- An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
- The acceleration of an object as
produced by a net force is directly proportional to the magnitude
of the net force, in the same direction as the net force, and
inversely proportional to the mass of the object.

In terms of an equation, the net force is equal to the product of the object's mass and its acceleration.

F_{net}= m × a - For every action, there is an equal and opposite reaction. That is, forces come in pairs.

- A man standing on the ground holds a rope that goes over a pulley and down to a 1,200 kg piano that is hanging in the air. How much force does the man have to provide to keep the piano from falling? If the man has a mass of 72 kg, can he do it?
- A 1.97 lb book is resting on a 21.32 lb table. What is the normal force on the floor?
- A lady pulls a cart with a force of 1598 N. Neglecting friction, if the cart changes from resting to a speed of 1.2 m/s in a distance of 1.113 m, what is the total mass of the cart?
- A man sees a 7.1 kg cart about to bump into a wall at 0.4 m/s. If the cart is 0.49 m from the wall when he grabs it, how much force must he apply to stop it before it hits?
- If you drop a penny from the top of the Empire State Building it can do some damage to someone on the ground. Calculate how fast it is going when it is about 1.6 m from the ground (a typical height). Then calculate the force that a 1.1 g penny exerts when it decelerates through someone’s skull in 1.2 cm. The Empire State Building is 381 m tall.

- A 3.4 kg mass and a 7.1 kg mass are tied to a light string and hung over a frictionless pulley. What is their acceleration?
- A 5 kg mass and a 8.9 kg mass are tied to a light string and hung over a frictionless pulley. How fast is the heavier mass falling 0.73 seconds after they are released from rest?
- A 9.1 kg mass and a 14.7 kg mass are tied to a light string and hung over a frictionless pulley. How fast is the lighter mass moving upward 0.66 seconds after they are released from rest?
- An unknown mass and a 5.5 kg mass are tied to a light string and hung over a frictionless pulley. If the tension in the string is 27.67 N, what is the unknown mass?