A dinner plate falls vertically to the floor and breaks up into three pieces, which slide horizontally along the floor. immediat

Question

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A dinner plate falls vertically to the floor and breaks up into three pieces, which slide horizontally along the floor. immediat

ely after the impact, a 200-g piece moves along the +x-axis with a speed of 2.00 m/s, a 235-g piece moves along the +y-axis with a speed of 1.50 m/s. the third piece has a mass of 100 g. what is the speed of the third piece?

Physics

2 answers:

Ostrovityanka [3.2K] · Answer 1 · 2026-03-10T02:03:08+03:00

The velocity of the third piece weighing $100{\text{ g}}$ equals $\boxed{5.33{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}}$ .

Explanation:

After the plate has fallen straight down and fragmented into three sections, they move horizontally in different directions.

The initial piece with a mass of $200{\text{ g}}$ is moving on the x-axis at a speed of $2{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}$ , while the second piece with a mass of $235{\text{ g}}$ moves vertically on the y-axis at a speed of $1.5{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}$ .

We need to determine the speed of the third part weighing $100{\text{ g}}$ .

Assuming the x-y plane represents the horizontal surface, there was no prior momentum before impact.

Designate the third piece’s velocity components as ${v_x}$ and ${v_y}$ , and the resultant velocity $v$ creates an angle of $\phi$ from the negative x-axis as depicted in Figure 1.

Using the principle of conservation of momentum gives the following equation:

$\begin{aligned}100{v_x}+2\left({200}\right)&=0\\100{v_x}&=-400\\{v_x}&=-4{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}\\\end{aligned}$

A second equation based on conservation of momentum can be expressed as:

$\begin{aligned}100{v_y}+1.5\left({235}\right)&=0\\100{v_y}&=-352.5\\{v_y}&=-3.525{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}\\\end{aligned}$

The velocity $v$ that the third piece travels is determined as follows:

$\begin{aligned}v&=\sqrt{v_x^2+v_y^2}\\&=\sqrt{{{\left({-4}\right)}^2}+{{\left({-3.525}\right)}^2}}\\&=5.33{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}\\\end{aligned}$

Thus, the speed of the third piece is $5.33{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}$ .

Hence, the velocity of the third piece that has a mass of $100{\text{ g}}$ amounts to $\boxed{5.33{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}}$ .

Learn More:

1. Speed and momentum

2. Linear momentum

3. Velocity and Momentum

Answer Details:

Grade: High School

Subject: Physics

Chapter: Momentum

Keywords:

Plate, momentum, falls, collision, slide, impact, 200 g, 2 m/s, 235 g, 1.50 m/s, 100 g, direction, motion, horizontal, force, x-axis, y-axis, vertically, floor, breaks, three, pieces.

serg [3.5K] · Answer 2 · 2026-03-10T02:03:14+03:00

<span>We will apply the momentum-impulse theorem here. The total momentum along the x-direction is defined as p_(f) = p_(1) + p_(2) + p_(3) = 0.
Therefore, p_(1x) = m1v1 = 0.2 * 2 = 0.4. Additionally, p_(2x) = m2v2 = 0 and p_(3x) = m3v3 = 0.1 *v3, where v3 represents the unknown speed and m3 signifies the mass of the third object, which has an unspecified velocity.
In the same way, for the particle of 235g, the y-component of the total momentum is described with p_(fy) = p_(1y) + p_(2y) + p_(3y) = 0.
Thus, p_(1y) = 0, p_(2y) = m2v2 = 0.235 * 1.5 = 0.3525 and p_(3y) = m3v3 = 0.1 * v3, where m3 is the mass of the third piece.
Consequently, p_(fx) = p_(1x) + p_(2x) + p_(3x) = 0.4 + 0.1v3; yielding v3 = 0.4/-0.1 = - 4.
Similarly, p_(fy) = 0.3525 + 0.1v3; thus v3 = - 0.3525/0.1 = -3.525.
Therefore, the x-component of the speed of the third piece is v_3x = -4 and the y-component is v_3y = 3.525.
The overall speed is calculated as follows: resultant = âš (-4)^2 + (-3.525)^2 = 5.335</span>