child pulls a string attached to a toy of mass 0.4 kg on a low horizontal table. The toy moves in a straight line towards the table edge with a constant acceleration of magnitude 1.5 m s−2 . The string is taut and makes an angle of 25◦ with the horizontal, as shown in the diagram attached. The coefficient of sliding friction between the toy and the table is 0.1. Take the magnitude of the acceleration due to gravity to be 9.8 m s−2 . Model the toy as a particle and the string as a model string. In your response to this question, underline vectors to distinguish them from scalar quantities. Where the magnitude of a vector is unknown, use the vector letter to represent the magnitude: for example, write the magnitude of a vector A as A.
A child pulls a string attached to a toy of mass 0.4 kg on a low horizontal table. The toy moves in a straight line towards the table edge with a constant acceleration of magnitude 1.5 m s−2 . The string is taut and makes an angle of 25◦ with the horizontal, as shown in the diagram attached.
The coefficient of sliding friction between the toy and the table is 0.1. Take the magnitude of the acceleration due to gravity to be 9.8 m s−2 . Model the toy as a particle and the string as a model string. In your response to this question, underline vectors to distinguish them from scalar quantities. Where the magnitude of a vector is unknown, use the vector letter to represent the magnitude: for example, write the magnitude of a vector A as A.
(a) (i) State the four forces that act on the toy.
(ii) Draw a force diagram that represents the four forces, labelling the forces clearly.
(iii) Take the Cartesian unit vectors i and j to point horizontally in the direction of motion of the toy and vertically upwards respectively, as shown above. Write down expressions (in terms of i and j) for the component forms of the four forces acting on the toy.
(iv) Write down the vector equation obtained by applying Newton’s second law of motion to the toy. Hence, or otherwise, find the magnitude of the pulling force exerted by the child, to two significant figures.
(b) The toy is initially at rest, and it falls off the table after 1.3 seconds. Calculate, to two significant figures, the initial distance of the toy from the table edge.
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