Worksheet: Work Done by a Variable Force

Q1:

The figure shows the magnitude of a force acting on a body as it moves a distance . Given that the force is measured in newtons, and the distance is measured in meters, determine, the work done in joules by the force to move the body from to .

• A 99 J
• B 24.75 J
• C 74.25 J
• D 49.5 J

Q2:

The figure shows the magnitude of a force acting on a body as it moves a distance . Given that the force is measured in newtons, and the distance is measured in meters, determine, the work done in joules by the force to move the body from to .

• A 77 J
• B 19.25 J
• C 57.75 J
• D 38.5 J

Q3:

A body moves along the -axis under the action of a force, . Given that , where m is the displacement from the origin, determine the work done on the body by when the body moves from to .

Q4:

A body moves along the -axis under the action of a force, . Given that , where m is the displacement from the origin, determine the work done on the body by when the body moves from to .

Q5:

From Newtonβs universal gravitational law, we know that a body at a distance from the center of the Earth is affected by a gravitational force such that , where is a constant. Assuming the radius of the Earth is 6371 km, find the magnitude of the work required for a satellite of mass 793 kg to achieve vertical takeoff from the ground and reach orbit at an altitude of 831 km.

• A 33β681β353.33 kg-wtβkm
• B 9β521β459.5 kg-wtβkm
• C 3β886β310 kg-wtβkm
• D 582β946.5 kg-wtβkm
• E 5β635β149.5 kg-wtβkm

Q6:

From Newtonβs universal gravitational law, we know that a body at a distance from the center of the Earth is affected by a gravitational force such that , where is a constant. Assuming the radius of the Earth is 6371 km, find the magnitude of the work required for a satellite of mass 754 kg to achieve vertical takeoff from the ground and reach orbit at an altitude of 831 km.

• A 32β024β893.33 kg-wtβkm
• B 9β053β191 kg-wtβkm
• C 3β695β180 kg-wtβkm
• D 554β277 kg-wtβkm
• E 5β358β011 kg-wtβkm

Q7:

From Newtonβs universal gravitational law, we know that a body at a distance from the center of the Earth is affected by a gravitational force such that , where is a constant. Assuming the radius of the Earth is 6371 km, find the magnitude of the work required for a satellite of mass 728 kg to achieve vertical takeoff from the ground and reach orbit at an altitude of 831 km.

• A 30β920β586.67 kg-wtβkm
• B 8β741β012 kg-wtβkm
• C 3β567β760 kg-wtβkm
• D 535β164 kg-wtβkm
• E 5β173β252 kg-wtβkm