6.1 Solving Problems with Newton’s Laws

Now calculate the scale reading when the elevator accelerates downward at a rate of $1.20 \text{m}/\text{s}^{2} .$

Calculate the acceleration of the system, and the tension in the string, when the masses are $m_{1} = 5.00 \text{kg}$ and $m_{2} = 3.00 \text{kg} .$

Determine a general formula in terms of $m_{1} , m_{2}$ and g for calculating the tension in the string for the Atwood machine shown above.

The soccer player stops after completing the play described above, but now notices that the ball is in position to be stolen. If she now experiences a force of 126 N to attempt to steal the ball, which is 2.00 m away from her, how long will it take her to get to the ball?

Find the direction of the resultant for the 1.50-kg model helicopter.

If atmospheric resistance is neglected, find the maximum height for the mortar shell. Is calculus required for this solution?

To simulate the apparent weightlessness of space orbit, astronauts are trained in the hold of a cargo aircraft that is accelerating downward at g. Why do they appear to be weightless, as measured by standing on a bathroom scale, in this accelerated frame of reference? Is there any difference between their apparent weightlessness in orbit and in the aircraft?

A 30.0-kg girl in a swing is pushed to one side and held at rest by a horizontal force $\overset{\rightarrow}{F}$ so that the swing ropes are $30.0 °$ with respect to the vertical. (a) Calculate the tension in each of the two ropes supporting the swing under these conditions. (b) Calculate the magnitude of $\overset{\rightarrow}{F} .$

Three forces act on an object, considered to be a particle, which moves with constant velocity $v = \left(3 \hat{i} - 2 \hat{j}\right) \text{m}/\text{s} .$ Two of the forces are $\overset{\rightarrow}{F}_{1} = \left(3 \hat{i} + 5 \hat{j}\right) \text{N}$ and $\overset{\rightarrow}{F}_{2} = \left(4 \hat{i} - 7 \hat{j}\right) \text{N} .$ Find the third force.

A 35.0-kg dolphin accelerates opposite to the motion from 12.0 to 7.50 m/s in 2.30 s to join another dolphin in play. What average force was exerted to slow the first dolphin if it was moving horizontally? (The gravitational force is balanced by the buoyant force of the water.)

A large rocket has a mass of $2.00 \times 10^{6} \text{kg}$ at takeoff, and its engines produce a thrust of $3.50 \times 10^{7} \text{N} .$ (a) Find its initial acceleration if it takes off vertically. (b) How long does it take to reach a velocity of 120 km/h straight up, assuming constant mass and thrust?

A 2.50-kg fireworks shell is fired straight up from a mortar and reaches a height of 110.0 m. (a) Neglecting air resistance (a poor assumption, but we will make it for this example), calculate the shell’s velocity when it leaves the mortar. (b) The mortar itself is a tube 0.450 m long. Calculate the average acceleration of the shell in the tube as it goes from zero to the velocity found in (a). (c…

An elevator filled with passengers has a mass of $1.70 \times 10^{3} \text{kg}$. (a) The elevator accelerates upward from rest at a rate of $1.20 \text{m}/\text{s}^{2}$ for 1.50 s. Calculate the tension in the cable supporting the elevator. (b) The elevator continues upward at constant velocity for 8.50 s. What is the tension in the cable during this time? (c) The elevator accelerates opposite to the motion at a rate of $0.600 \text{m}/\text{s}^{2}$ for 3.00 s. What is the tensio…

A student’s backpack, full of textbooks, is hung from a spring scale attached to the ceiling of an elevator. When the elevator is accelerating downward at $3.8 \text{m}/\text{s}^{2}$, the scale reads 60 N. (a) What is the mass of the backpack? (b) What does the scale read if the elevator moves upward while speeding up at a rate $3.8 \text{m}/\text{s}^{2}$? (c) What does the scale read if the elevator moves upward at constant velocity? (d) If the el…

A roller coaster car starts from rest at the top of a track 30.0 m long and inclined at $20.0 °$ to the horizontal. Assume that friction can be ignored. (a) What is the acceleration of the car? (b) How much time elapses before it reaches the bottom of the track?