Question

Dinah is playing cards with her friends, and it is her turn to deal. A card with a mass of 2.3 g slides 0.35 m along the table before it stops. If the coefficient of kinetic friction between the card and the table is 0.24, what was the initial speed of the card as it left Dinah’s hand?

-provide a full explanation

Answer 1

The initial speed of the card as it left Dinah's hand was 0.82 m/s.

Step-by-step explanation:

To find the initial speed of the card as it left Dinah's hand, we can use the equation for kinetic friction:

frictional force = coefficient of kinetic friction * normal force

The normal force on the card is equal to its weight, which is given by mass * acceleration due to gravity. Since the card is moving at a constant speed, the frictional force is equal to the force required to balance the net force acting on the card. This force is given by mass * acceleration. Setting the two equations equal to each other and solving for the initial speed, we get:

initial speed = (coefficient of kinetic friction * mass * acceleration due to gravity * distance) / mass

Plugging in the given values, we have:

initial speed = (0.24 * 2.3 g * 9.8
`m/s^2` * 0.35 m) / 2.3 g

initial speed = 0.24 * 9.8
`m/s^2` * 0.35 m = 0.82 m/s

Therefore, the initial speed of the card as it left Dinah's hand was 0.82 m/s.