Question

In Problems 64 and 65 you are given the equation used to solve a problem. For each of these, you are to
a. Write a realistic problem for which this is the correct equation. Be sure that the answer your problem requests is consistent with the equation given.
b. Finish the solution of the problem.
65. (1500 kg)(9.8 m/s²) - 11,760 N = (1500 kg) v²/(200 m)

Short answer

a) A 1500 kg vehicle is running on circular track with radius 200 m. if Normal force is 11760 N then find the velocity of the vehicle.

b) Velocity of vehicle is 19.8 m/sec

Step-by-step solution

Part(a) Step 1: Given information

The equation is (1500 kg)(9.8 m/s²) - 11,760 N = (1500 kg) v²/(200 m)

Part(a) Step 2: Explanation

In the given equation we see mass is 1500 kg, radius is 200 m and velocity is unknown .

We can frame the question As

A 1500 kg vehicle is running on circular track with radius 200 m. if Normal force is 11760 N then find the velocity of the vehicle.

Part(b) Step 1: Given Information

The equation is (1500 kg)(9.8 m/s²) - 11,760 N = (1500 kg) v²/(200 m)

Part(b) Step 2 : Explanation

Solve the given equation

(1500 kg)(9.8 m/s²) - 11,760 N = (1500 kg) v²/(200 m)

$$\begin{gathered} \left(1500kg\right)(9.8m/s^2)-11760N=\frac{\left(1500kg\right)}{\left(200m\right)}{v}^2 \\ \frac{\left(1500kg\right)}{\left(200m\right)}{v}^2=14700N-11760N \\ {v}^2=\frac{\left(2940N\right)\left(200m\right)}{\left(1500kg\right)} \\ v=\sqrt{\frac{\left(2940N\right)\left(200m\right)}{\left(1500kg\right)}}=19.8m/s \end{gathered}$$