Question

A 10.0-kg object is initially moving east at 15.0 m/s. A force acts on it for 2.00 s, after which it moves northwest at 15.0 m/s. What is the magnitude and direction of the average force?

a) 18.0 N, northwest
b) 20.0 N, northwest
c) 22.5 N, northwest
d) 25.0 N, northwest

Answer 1

To find the magnitude and direction of the average force acting on the object, we can calculate the change in momentum and divide it by the time interval. The magnitude of the average force is 20.0 N in the northwest direction (option b).

Step-by-step explanation:

To find the magnitude and direction of the average force, we need to consider the change in momentum of the object. The initial momentum is the product of the mass (10.0 kg) and the velocity (15.0 m/s east), which is 150.0 kg·m/s east. The final momentum is the product of the mass (10.0 kg) and the velocity (15.0 m/s northwest). We can divide the change in momentum by the time interval (2.00 s) to find the average force:

Magnitude of average force = Change in momentum / Time interval = (Final momentum - Initial momentum) / Time interval

The change in momentum is the vector difference between the final and initial momenta:

Change in momentum = Final momentum - Initial momentum

Finally, we can determine the direction of the average force based on the change in momentum. Since the object is moving from east to northwest, the force must have acted in the northwest direction. Therefore, the answer is:

b) 20.0 N, northwest