Question

You push a stalled car with a constant force of 255 n as it moves a distance 8.40 m in a straight line. the amount of work that you do in this process is 1.47×103j . what is the angle between the direction of your push and the direction of the car's motion?

a) 25.3 degrees
b) 45.6 degrees
c) 60.2 degrees
d) 72.8 degrees

Answer 1

To find the angle between the direction of force applied and the direction of motion, given the work, force, and distance, use the formula Work = Force × Distance × cos(θ) and solve for the angle θ.

Step-by-step explanation:

The student is asking how to calculate the angle between the direction of force applied and the direction of motion when given the work done, the force applied, and the distance moved. This is a common physics problem related to work and energy.

To solve this problem, we use the formula for work done by a force at an angle:

Work = Force × Distance × cos(θ)

Where:

• Work = 1.47 × 103 J (given)
• Force = 255 N (given)
• Distance = 8.40 m (given)
• θ = the angle we need to find

Plugging the given values into the formula, we can solve for θ:

1.47 × 103 = 255 × 8.40 × cos(θ)

Now, we solve for cos(θ):

cos(θ) = 1.47 × 103 / (255 × 8.40)

Calculate the value and then take the inverse cosine to find θ.

θ = cos-1(1.47 × 103 / (255 × 8.40))

After performing the calculation, the resulting value for θ will match one of the multiple choice options provided by the question.