Physics 2003 JAMB Past Questions - Question 1: A bead travelling on a straight wire is brought to rest at 0.2m by friction. If the mass of the bead is 0.01kg and the coefficient of friction between the bead and the wire is 0.1, determine the work done by the friction

Correct Answer

C

Explanation

To determine the work done by friction to bring the bead to rest at 0.2 meters, we can use the work-energy principle. The work done by friction will be equal to the change in kinetic energy of the bead as it comes to a stop.

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the initial kinetic energy of the bead is given by:

\(KE_{\text{initial}} = \frac{1}{2}mv^2\)

Where:
\(m\) = mass of the bead = 0.01 kg
\(v\) = initial velocity of the bead (which is not given)

The final kinetic energy of the bead is zero because it comes to rest.

Therefore, the work done by friction is given by:

\(W_{\text{friction}} = KE_{\text{final}} - KE_{\text{initial}}\)

\(W_{\text{friction}} = 0 - KE_{\text{initial}}\)

Now, we need to find the initial velocity of the bead. We can use the equation of motion:

\(v^2 = u^2 + 2as\)

Where:
\(v\) = final velocity (0 m/s, since it comes to rest)
\(u\) = initial velocity (which we want to find)
\(a\) = acceleration due to friction
\(s\) = displacement (0.2 m)

The acceleration due to friction can be calculated using Newton's second law:

\(F_{\text{friction}} = \mu \cdot N\)

Where:
\(F_{\text{friction}}\) = force of friction
\(\mu\) = coefficient of friction = 0.1
\(N\) = normal force (equal to the weight of the bead, \(mg\))

\(N = mg\)
\(N = 0.01 kg \cdot 9.8 m/s^2\) (acceleration due to gravity)

Now, calculate the force of friction:

\(F_{\text{friction}} = 0.1 \cdot 0.01 kg \cdot 9.8 m/s^2\)

Next, we can use Newton's second law to find the acceleration:

\(F_{\text{friction}} = ma\)

\(0.01 kg \cdot 9.8 m/s^2 = 0.001 kg \cdot a\)

Now, we have the acceleration (\(a\)).

Now, use the equation of motion to find the initial velocity (\(u\)):

\(u^2 = 0^2 + 2 \cdot a \cdot 0.2 m\)

Finally, you can calculate the work done by friction:

\(W_{\text{friction}} = 0 - \frac{1}{2} \cdot 0.01 kg \cdot u^2\)

Substitute the value of \(u\) and calculate \(W_{\text{friction}}\).

Note: Since the problem doesn't provide the initial velocity (\(u\)) of the bead, you may need additional information or assumptions to calculate the exact work done by friction.