Master Algebra with our Comprehensive Practice Problems

Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force ${\displaystyle \overrightarrow{F}}$ The magnitude of the tension in the string between blocks B and C is T=3.00N. Each block has mass m=0.400kg. 
What is the magnitude F of the force? 
What is the tension in the string between block A and block B?

Block A in the fig. 5.58 weighs 1.20N and Block B weighs3.60N. The Coefficient of kinetic friction between all surfaces is0. 300. Find the magnitude of the horizontal force F necessary to drag black B to the left at a constant speed a) if A rest on B and moves with it (fig. 5.28am). b) If A is held at rest.

On a long flat firing range, a projectile is fired with an initial speed of 75.2 m/s at an angle of 34.5 degrees above the horizontal. Determine (a) the maximum height reached by the projectile, (b) the total time in the air, (c) the total horizontal distance covered (that is, the range) and (d) the velocity of the projectile 1.50 s after firing.

An automobile has a mass of 1200 kg. What is its kinetic energy, in kJ, relative to the road when traveling at a velocity of 50 km/h? If the vehicle accelerates to 100 km/h, what is the change in kinetic energy, in kJ?

Racing Racing Cars A and B are traveling on circular portions of a racetrack. In the instant shown, the speed of A is decreasing auto rate of ${\displaystyle 8\frac{m}{s^2}}$, and the speed of B is increasing at the rate of ${\displaystyle 3\frac{m}{s^2}}$. For the positions shown, determine (a) the velocity of B relative to A, (b) the acceleration of B relative to A.

A clay vase on a potter's wheel experiences an angular acceleration of ${\displaystyle 8.00\frac{rad}{{\sec }^2}}$ due to the application of 10.0Nm net torque. Find the total moment of inertia of the vase and the potter's wheel.

A coin with a diameter of 2.40cm is dropped on edge on to a horizontal surface. The coin starts out with an initial angular speed of 18.0 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 1.90 rad/s, how far does the coin roll before coming to rest?

A 2.10 kg book is raised 2.20 m above the ground by a 1.60 m tall person. What is the book's potential energy in relation to:
(a) the ground and 
(b) the top of the persons

A weatherman carried an aneroid barometer from the groundfloor to his office atop a tower. On the ground level, the barometer read 30.150 in Hg absolute; topside it read 28.607 in hg absolute. Assume that the average atmospheric air density was 0.075lb/ft3, estimate the height of the building.

At the beginning of a laboratory experiment, the temperature of a substance is $-{12.6}^{\circ }C$. During the experiment, the temperature of the substance decreases ${7.5}^{\circ }C$. What is the final temperature of the substance?

Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series.
${\displaystyle \sum _{n=1}^{\mathrm{\infty }}\frac{1}{{(2n+3)}^3}}$

Tell whether the function represents exponential growth or decay. $w(x)=0.72\cdot 2^x$

The garden is made up of a rectangular patch of grass and two semi-circular vegetable patches. If the dimensions of the rectangular patch are 16 m (length) and 8 m (width) respectively, calculate: 1) the perimeter of the garden. 
2) the total area of the garden.

If the exponential function f(x) has values of f(-1)=8 and f(8.5)=87, then find the value of f(3), to the nearest hundredth.