Question

A horizontal net force \[F\] is exerted on an object at rest. The object starts at \[x = 0\,\text m\] and has a speed of \[4.0\,\dfrac{\text m}{\text s}\] after moving \[2.0\,\text m\] along a horizontal frictionless surface. The net force \[F\] as a function of the object's position \[x\] is shown below. Net horizontal force (N) vs. horizontal position (m) graph. Y-intercept is zero and it has a slope of 5 m/s. \[1\] \[2\] \[3\] \[4\] \[5\] \[6\] \[7\] \[10\] \[20\] \[30\] \[40\] \[\text{Force (N)}\] \[\text{Position (m)}\] Net horizontal force (N) vs. horizontal position (m) graph. Y-intercept is zero and it has a slope of 5 m/s. What is the mass of the object? Round answer to 2 significant digits.

Answer 1

The mass of the object is determined as 2.5 kg.

How to calculate the mass of the object?

The mass of the object is calculated by applying Newton's second law of motion as follows;

m = F / a

where;

• F is the net force on the object at a 2 m position
• a is the acceleration of the object

The acceleration of the object is calculated by applying the following kinematic equation as follows;

v² = u² + 2as

where;

• v is the final velocity
• u is the initial velocity
• s is the distance traveled

v² = 0 + 2as

a = v² / 2s

a = ( 4 m/s)² / (2 x 2 m)

a = 4 m/s²

The mass of the object is calculated as follows;

m = F / a

m = 10 N / 4 m/s²

m = 2.5 kg

The complete question is given below:

A horizontal net force F is exerted on an object at rest. The object starts at x= 0 m and has a speed of 4.0 m/s after moving 2.0 m along a horizontal frictionless surface. The net force F as a function of the object's position x is shown below.

what is the mass of the object?