Question

A box of mass 50 kg is at rest on a horizontal frictionless surface. A constant horizontal force F then acts on the box

and accelerates it to the right. It is observed that it takes the box 6. 9 seconds to travel 28 meters. What is the


magnitude of the force?

Answer 1

To calculate the force on the box, first use the displacement and time to find the acceleration, then apply Newton's Second Law with the box's mass to find the force, which is 58.5 newtons.

Step-by-step explanation:

The student is asking to find the magnitude of the force that accelerated a 50 kg box on a frictionless surface, given that it took 6.9 seconds to travel 28 meters. We can find this force by first determining the acceleration of the box using kinematic equations and then applying Newton's Second Law of motion (Force = mass × acceleration).

Step 1: Find the acceleration

To find acceleration, we use the kinematic equation for uniform acceleration: s = ut + ½at², where s is the displacement, u is the initial velocity (0 m/s, since the box starts from rest), t is the time, and a is the acceleration. We can rearrange this equation to solve for a:
a = 2s/t²

Step 2: Apply Newton's Second Law

Once we determine a, we can calculate the force using F = ma. Plugging the values in, we get the desired force.

Using the values provided (s = 28 m, t = 6.9 s):

a = 2×28/(6.9)² = 1.17 m/s²

Now applying Newton's Second Law with the calculated acceleration and the mass of 50 kg:

F = m×a = 50 kg × 1.17 m/s² = 58.5 N

Answer 2

The magnitude of the force is approximately 202.85 N.

Step-by-step explanation:

To find the magnitude of the force, we can use the equation F = m*a, where m is the mass and a is the acceleration. In this case, the box has a mass of 50 kg and is accelerated to the right. We can calculate the acceleration by using the equation a = (final velocity - initial velocity) / time. The initial velocity is 0 m/s since the box starts at rest, the final velocity is 28 m/s divided by the time of 6.9 seconds, giving us an acceleration of approximately 4.057 m/s². Now we can calculate the force by multiplying the mass by the acceleration: F = 50 kg * 4.057 m/s² = 202.85 N.