Lesson Worksheet: Motion of a Body on a Rough Plane Mathematics

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In this worksheet, we will practice studying the motion of a particle on horizontal and inclined rough planes against friction force.

Q1:

A body of mass 21 kg was placed on a rough horizontal plane. A horizontal force of magnitude 144.06 N acted on the body, causing a uniform acceleration of 4.9 m/s². Determine the coefficient of friction of the plane. Take .

Q2:

A body of mass 28 kg moves on a horizontal plane with an acceleration of magnitude 2.2 m/s². It is subjected to an applied force of 155 N whose direction is given in the figure. Calculate the coefficient of kinetic friction rounding the result to the nearest two decimal places. Take the acceleration due to gravity .

Q3:

A car of mass 3.6 metric tons was moving along a straight horizontal road at 18 km/h when its engine cut out. Given that it traveled a further 180 m before it stopped moving, find the magnitude of the resistance to the movement of the car.

Q4:

A body of mass 440 g was resting on a rough horizontal plane whose coefficient of friction was . The body was dragged across the plane by the action of a horizontal force. Given that the action of this force resulted in a uniform acceleration of 170 cm/s², find the magnitude of the force. Take the acceleration due to gravity .

Q5:

A body of 12 kg was placed on a rough horizontal plane. It was pulled by a force whose line of action made an angle of upward of the plane where . If the body, starting from rest, moved a distance of 804 cm in 4 seconds and the coefficient of friction was , find the magnitude of the pulling force. Take the acceleration due to gravity .

Q6:

A horse was pulling a wooden block along a section of horizontal ground. The pulling force of the horse was 22 kg-wt which was acting on the block at an angle of to the vertical. Given that the block was moving uniformly, determine the magnitude of the friction acting on the block.

A22 kg-wt
B kg-wt
C kg-wt
D11 kg-wt

Q7:

In a factory, boxes are transferred from one area to another via a rough inclined slope of length 13 m and height 12 m. The boxes are released from rest at the top of the slope and left to slide down freely. Given that the coefficient of friction between the plane and a box is 0.27 , find the speed of a box when it reaches the bottom of the slope rounded to two decimal places. Take the acceleration due to gravity .

Q8:

A body of mass 74 kg was projected at 8.5 m/s along the line of greatest slope up a plane inclined at to the horizontal. Given that the resistance of the plane to its motion was 7.4 N, find the distance the body traveled until it came to rest. Take .

Q9:

A body of mass kg was placed on a plane inclined at to the horizontal. A force of magnitude N was acting on the body along the line of greatest slope up the plane. As a result, the body accelerated uniformly at m/s² up the plane. If the magnitude of the force acting on the body is halved while maintaining its original direction, the body will move down the plane at m/s². Given that the resistance of the plane to the body’s movement is N in both cases, determine the values of and , rounding the results to the nearest two decimal places. Take .

Q10:

A body of mass kg is placed on a rough horizontal plane. The coefficient of static friction between the body and the plane is and the coefficient of kinetic friction is . A force is acting on the body where its line of action makes an angle of to the horizontal. The force causes the body to be on the point of moving. If the magnitude of the force is increased from to , the body would start moving and accelerate at m/s². Find and . Take .

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