6. Intro to Forces (Dynamics)

A hockey puck with mass $0.160$ kg is at rest at the origin ($x=0$) on the horizontal, frictionless surface of the rink. At time $t=0$ a player applies a force of $0.250$ N to the puck, parallel to the $x$-axis; she continues to apply this force until $t=2.00$ s. What are the position and speed of the puck at $t=2.00$ s?

A small $8.00$-kg rocket burns fuel that exerts a time-varying upward force on the rocket (assume constant mass) as the rocket moves upward from the launch pad. This force obeys the equation $F=A+B{t}^2$. Measurements show that at $t=0$, the force is $100.0$ N, and at the end of the first $2.00$ s, it is $150.0$ N. Find the constants $A$ and $B$, including their SI units.

A $4.50$-kg experimental cart undergoes an acceleration in a straight line (the $x$-axis). The graph in Fig. E$4.13$ shows this acceleration as a function of time. During what times is the net force on the cart a constant?

A $4.50$-kg experimental cart undergoes an acceleration in a straight line (the $x$-axis). The graph in Fig. E$4.13$ shows this acceleration as a function of time. Find the maximum net force on this cart. When does this maximum force occur?

A hockey puck with mass $0.160$ kg is at rest at the origin ($x = 0$) on the horizontal, frictionless surface of the rink. At time $t = 0$ a player applies a force of $0.250$ N to the puck, parallel to the $x$-axis; she continues to apply this force until $t = 2.00$ s. If the same force is again applied at $t=5.00$ s, what are the position and speed of the puck at $t=7.00$ s?

A dockworker applies a constant horizontal force of $80.0$ N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves $11.0$ m in $5.00$ s. What is the mass of the block of ice?

A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude $48.0$ N to the box and produces an acceleration of magnitude $2.20$ m/s², what is the mass of the box?

Due to a jaw injury, a patient must wear a strap (Fig. E$4.3$) that produces a net upward force of $5.00$ N on his chin. The tension is the same throughout the strap. To what tension must the strap be adjusted to provide the necessary upward force?

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To extricate an SUV stuck in the mud, workmen use three horizontal ropes, producing the force vectors shown in Fig. E$4.2$. Use the components to find the magnitude and direction of the resultant of the three pulls.

To extricate an SUV stuck in the mud, workmen use three horizontal ropes, producing the force vectors shown in Fig. E$4.2$. Find the $x$- and $y$-components of each of the three pulls.

Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is $60.0$°. If Rover exerts a force of $270$ N and Fido exerts a force of $300$ N, find the magnitude of the resultant force and the angle it makes with Rover's rope.