Video Transcript
A body of mass 900 grams was projected vertically upwards at 6.4 meters per second. Find the work done by the weight of the body during the first five seconds of the motion of the body. Take 𝑔 equal to 9.8 meters per second squared.
In this question, we are asked to find the work done by the weight of the body. And we know this can be calculated by multiplying the force by the displacement. The standard units of force are newtons, and we measure displacement in meters. This gives us units of work of newton meters, which are more commonly referred to as joules. Let’s begin by sketching the scenario in this question.
We are told that a 900-gram body is projected vertically upwards at a velocity of 6.4 meters per second. The downward force that this body exerts will be equal to its weight. We know that 1000 grams is equal to one kilogram. And since the weight of a body is equal to its mass multiplied by gravity, the downward force is equal to 0.9 multiplied by 9.8, as 900 grams is equal to 0.9 kilograms and gravity is 9.8 meters per second squared. The downward force is therefore equal to 8.82 newtons.
In order to calculate the displacement of the body in the first five seconds, we will use the equations of motion or SUVAT equations. If we let the positive direction be vertically upwards, the initial velocity is equal to positive 6.4 meters per second. The acceleration 𝑎 is equal to negative 9.8 meters per second squared, as gravity is acting against the direction of motion. And we are interested in the displacement after five seconds. To calculate the displacement 𝑠, we will use the equation 𝑠 is equal to 𝑢𝑡 plus a half 𝑎𝑡 squared. Substituting in our values, we have 𝑠 is equal to 6.4 multiplied by five plus a half multiplied by negative 9.8 multiplied by five squared. This is equal to 32 minus 122.5, which in turn gives us negative 90.5. After five seconds, the displacement of the body is negative 90.5 meters. Therefore, the body is 90.5 meters below its start point.
Since the force 𝐹 is also acting in the negative direction, this will also have a negative value. As we defined vertically upwards to be the positive direction, the work done is equal to negative 8.82 multiplied by negative 90.5. Multiplying two negative numbers gives a positive answer, in this case 798.21. The work done by the weight of the body during the first five seconds of motion is 798.21 joules.
