Lesson Worksheet: Motion of a Body on a Smooth Inclined Plane Mathematics

In this worksheet, we will practice solving problems involving moving a particle on a smooth inclined plane.

Q1:

A body of mass 0.7 kg was placed on a smooth plane inclined at 66 to the horizontal and it was left to move freely under the effect of gravity, where the acceleration due to gravity is 9.8 m/s2. Find, to the nearest two decimal places, the magnitude of the reaction of the plane to the body.

Q2:

If a body of mass 3 kg was placed on a smooth plane inclined at 17 to the horizontal and was left to move freely, determine its acceleration to the nearest two decimal places.

Q3:

In a factory, boxes are transferred between two floors via a smooth inclined plane of length 15 m and height 12 m. The boxes are released from rest at the top of the slope and left to slide down freely. Taking 𝑔=9.8/ms, determine the velocity of a box when it reached the bottom of the plane.

Q4:

A body slides down a smooth plane under the action of its weight. Which of the following variables does the acceleration of the body depend on?

  • Athe weight of the body
  • Bthe mass of the body
  • Cthe angle of inclination of the plane
  • Dthe reaction of the plane

Q5:

A body of mass 484 g was placed on a smooth plane inclined at an angle 𝜃 to the horizontal, where sin𝜃=35. Given that a force of 484 g-wt was acting on the body parallel to the line of greatest slope up the plane, find the acceleration of motion. Consider the acceleration due to gravity to be 9.8 m/s2.

Q6:

A body of mass 1.4 kg was placed on a smooth plane inclined 45 to the horizontal. If a force of 59 N is acting on the body upward along the line of greatest slope of the plane, determine the acceleration of the body rounded to the nearest two decimal places. Take 𝑔=9.8/ms

Q7:

A body of mass 9 kg was moving along the line of greatest slope of a smooth plane inclined at 60 to the horizontal. A force of 3 kg-wt was acting on the body, where the line of action of the force was directed toward the plane at 30 upward of the horizontal. Find the magnitude of the normal reaction of the plane on the body. Take 𝑔=9.8/ms.

  • A63 kg-wt
  • B6 kg-wt
  • C33 kg-wt
  • D3 kg-wt

Q8:

A body of mass 205 kg was left to slide down a plane inclined at 45 to the horizontal. A force started acting on the body causing its acceleration to halve. Given that the line of action of the force made an angle of 45 with the line of greatest slope of the plane and that they both lie in the same vertical plane, find the magnitude of this force. Consider the acceleration due to gravity to be 9.8 m/s2.

Q9:

A body of mass 9 kg is released from rest on a smooth inclined plane. It moves a distance of 25.2 m in the first 4 seconds of its motion. If the body is projected upward along a line of greatest slope on the same plane, with an initial velocity of 12.6 m/s, how far does it travel before coming to instantaneous rest? Take 𝑔=9.8/ms.

Q10:

A body of mass 103 kg was placed on a smooth plane inclined at 30 to the horizontal. A horizontal force of 126 N directed toward the plane was acting on the body such that the line of action of the force and the line of greatest slope of the plane all lie in the same vertical plane. After moving for 7 seconds, the body reached a speed 𝑣, at which point the force stopped acting, and the body continued moving until it momentarily came to rest 𝑡 seconds after the force stopped acting. Find 𝑣 and 𝑡. Take 𝑔=9.8/ms.

  • A𝑣=9.8/ms, 𝑡=1s
  • B𝑣=4.9/ms, 𝑡=1s
  • C𝑣=16.62/ms, 𝑡=3.39s
  • D𝑣=9.8/ms, 𝑡=2s

This lesson includes 19 additional questions and 211 additional question variations for subscribers.

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