How Do Newton's Laws Apply to Real-World Physics Problems?

[cmculbert]

Homework Statement

1) A freight train has a mass of 1.5 x 10^7 kg. If the locomotive can exert a constant pull of 7.5 x 10^5 N, how long does it take to increase the speed of the train from rest to 80 km/h?


2) A 5.0 g bullet leaves the muzzle of a rifle with a speed of 320 m/s. What force (assumed constant) is exerted on the bullet while it is traveling down the 0.82 m long barrel of the rifle?


3)A block of mass m = 2.0 kg is held in equilibrium on an incline of angle theta = 60 degrees by the horizontal force F. (a) Determine the value of F. (b) Determine the normal force exerted by the incline of on the block (ignore friction).


4)A shopper in a supermarket pushes a loaded cart with a horizontal force of 10 N. The cart has a mass of 30 kg. (a)How far will it move in 3.0 s, starting from rest? (ignore friction) (b)How far will it move in 3.0 s if the shopper places her 30 N child in the cart before she begins to push it?


5)Two objects of masses 10.0 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley. The 5.00 kg object lies on a smooth incline of angle 40.0 degrees. Find the acceleration of the 5.00 kg object and the tension in the string.

Homework Equations

1) F=ma
2) w=mg
3) ?

The Attempt at a Solution

 

[mg0stisha]

First, show your attempts at solving all of these.

 

[tomcue]

1) Using Newton's second law, F=ma, we can rearrange the equation to solve for time: t=mv/F. Plugging in the given values, we get t=(1.5 x 10^7 kg)(80 km/h)/(7.5 x 10^5 N)= 160 seconds. Therefore, it would take 160 seconds for the train to reach a speed of 80 km/h.

2) Again, using Newton's second law, F=ma, we can solve for force by rearranging the equation: F=ma=m(v/t). Plugging in the given values, we get F=(5.0 g)(320 m/s)/(0.82 m)= 195,122.0 N. Therefore, the force exerted on the bullet while traveling down the barrel is 195,122.0 N.

3) (a) To find the value of F, we can use the equation F=mg*sin(theta), where m is the mass of the block and theta is the angle of the incline. Plugging in the given values, we get F=(2.0 kg)(9.8 m/s^2)*sin(60 degrees)= 19.6 N. Therefore, the value of F is 19.6 N.
(b) To find the normal force exerted by the incline, we can use the equation F=mg*cos(theta), where m is the mass of the block and theta is the angle of the incline. Plugging in the given values, we get F=(2.0 kg)(9.8 m/s^2)*cos(60 degrees)= 9.8 N. Therefore, the normal force exerted by the incline on the block is 9.8 N.

4) (a) Using Newton's second law, F=ma, we can solve for distance by rearranging the equation: d=(1/2)at^2. Plugging in the given values, we get d=(1/2)(10 N)(3.0 s)^2= 45 m. Therefore, the cart will move 45 m in 3.0 seconds.
(b) If the shopper's 30 N child is placed in the cart, the mass of the cart increases to 60 kg. Using the same equation as before, we get d=(1/2)(10 N)(3.0 s)^