Kathy Williams

2022-01-09

On an essentially frictionless, horizontal ice rink, a skater moving at 3.0 m/s encounters a rough patch that reduces her speed to 1.65 m/s due to a friction force that is $25\mathrm{\%}$ of her weight. Use the work–energy theorem to find the length of this rough patch.

Mary Nicholson

Beginner2022-01-10Added 38 answers

Step 1

The ice-skater experiences three forces during his/her transition across the rough patch: gravity, the normal force, and the force of friction. The first two cancel out, so that the force of friction is the total force acting on the skater, equal to${F}_{f}=\mu mg$ . Since $\frac{{F}_{f}}{m}g=\frac{1}{4}$ , we have $\mu =\frac{1}{4}$ . The friction is opposite to the displacement and so the work done by friction is ${W}_{f}=-\mu mgl$ , where l is the length of the rough patch.

$$

Now, if the initial and the final speeds of the skater were$v}_{i}=3\frac{m}{s$ and ${v}_{f}=1.65$ , respectively, by the work energy theorem we have

${W}_{\to t}={W}_{f}=-\mu mgl={K}_{f\in al}-{K}_{\in itial}=\frac{1}{2}m({v}_{f}^{2}-{v}_{i}^{2})\Rightarrow$

$l=\frac{1}{2\mu g}({v}_{i}^{2}-{v}_{f}^{2})$

$=\left(\frac{1}{2\cdot 0.25\cdot 9.8}({3}^{2}-{1.65}^{2})\right)m$

$=1.28m$

The ice-skater experiences three forces during his/her transition across the rough patch: gravity, the normal force, and the force of friction. The first two cancel out, so that the force of friction is the total force acting on the skater, equal to

Now, if the initial and the final speeds of the skater were

22+64

When a cold drink is taken from a refrigerator, its temperature is 5 degree C. After 25 minutes in a 20 degree C room its temperature has increased to 10 degree C. What is the temperature of the drink after 50 minutes?

How many minutes are there in $2\frac{3}{5}$ hours?

Find the answer for $64$ power $\frac{1}{6}$.

The following law describes the relationship between gas volume and pressure: ________. A)Boyle's law; B)Henry's law; C)Charles' law; D)Dalton's law

If an electric switch is open then no current flows through the circuit.

A)True;

B)FalseThe price elasticity of supply of a good is 0.8. Its price rises by 50 per cent. Calculate the percentage increase in its supply.

How many quarts are in 10 gallons?

When the net force acting on an object is zero, the total momentum of the system will:

A)remain constant;

B)increase with time;

C)decrease with time;

D)None of theseHow many centimeters are in four meters?

A notebook computer has a mass of 2.25 kilograms. About how many pounds does the notebook weigh?

If the dot product of two non-zero vectors is zero, then the vectors A)are parallel to each other. B)are perpendicular to each other. C)can have any orientation. D)are anti-parallel to each other.

Which is longer 5 miles or 10 kilometers?

9 grams is how many milligrams?

How to write $673.5$ in scientific notation?